3
3.0
Jun 28, 2018
06/18
by
Mourad Lazgham
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eye 3
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We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough)....
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1510.03584
4
4.0
Jun 30, 2018
06/18
by
Jean-Pierre Fouque; Ning Ning
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eye 4
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In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead of using two deterministic bounds, the uncertain volatility fluctuates between two stochastic bounds generated by its inherent stochastic volatility process. This brings better accuracy and is consistent with the observed volatility path such as for the VIX...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1702.05036
5
5.0
Jun 30, 2018
06/18
by
Wei Lin; Shenghong Li; Shane Chern
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eye 5
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In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First, we do not restrict the new parameter, letting the data speak as to its direction. The Generalized Methods of Moments suggests that the newly added parameter is to create varying volatility fluctuation in different period discovered in financial market....
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1703.06020
5
5.0
Jun 30, 2018
06/18
by
Ralph Rudd; Thomas A. McWalter; Joerg Kienitz; Eckhard Platen
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eye 5
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comment 0
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is usually performed using stochastic methods, e.g., Lloyd's algorithm or Competitive Learning Vector Quantization. In this paper, a new algorithm is proposed that allows RMQ to be applied to two-factor stochastic volatility models, which retains the efficiency of...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1704.06388
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16
Jun 27, 2018
06/18
by
Mykhaylo Shkolnikov; Ronnie Sircar; Thaleia Zariphopoulou
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We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae for the leading order and first order correction terms for the forward investment process and the...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1504.03209
6
6.0
Jun 29, 2018
06/18
by
Francesca Biagini; Andrea Mazzon; Thilo Meyer-Brandis
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eye 6
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We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). To justify $W^F$ from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles, see Jarrow, Protter and Shimbo (2010) and Biagini, F\"ollmer and Nedelcu (2014), by showing the existence of a flow...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1611.01440
3
3.0
Jun 30, 2018
06/18
by
Wai-Ki Ching; Jia-Wen Gu; Harry Zheng
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In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1409.1393
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12
Jun 28, 2018
06/18
by
Matteo Burzoni; Marco Frittelli; Marco Maggis
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eye 12
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In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path $\omega \in \Omega$, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1506.06608
5
5.0
Jun 29, 2018
06/18
by
Hannes Hoffmann; Thilo Meyer-Brandis; Gregor Svindland
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eye 5
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We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate case in F\"ollmer (2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1609.07903
6
6.0
Jun 29, 2018
06/18
by
David Hobson; Alex S. L. Tse; Yeqi Zhu
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eye 6
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In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation, and find that the form of the solution (whether the problem is well-posed, whether the problem is well-posed only for large transaction costs, whether the no-transaction wedge lies in the first, second or fourth quadrants) depends only on a quadratic whose...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1612.00720
6
6.0
Jun 29, 2018
06/18
by
K. Kanjamapornkul; R. Pinčák
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eye 6
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We provide the proof that the space of time series data is a Kolmogorov space with $T_{0}$-separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes from the rotation of data around price and time axis by defining a new extradimension to time series data. We show that there exist hidden eight dimensions in Kolmogorov space for...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1606.03901
8
8.0
Jun 28, 2018
06/18
by
Robert Fernholz
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eye 8
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Long-term relative arbitrage exists in markets where the excess growth rate of the market portfolio is bounded away from zero. Here it is shown that under a time-homogeneity hypothesis this condition will also imply the existence of relative arbitrage over arbitrarily short intervals.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1510.02292
7
7.0
Jun 28, 2018
06/18
by
Takanori Adachi
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eye 7
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We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formulae in the language, which is expected to be clues of analyzing the moments that some stochastic jumps such as financial crises occur based on knowledge and belief of individuals...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1512.00227
5
5.0
Jun 29, 2018
06/18
by
Claudia Ceci; Katia Colaneri; Alessandra Cretarola
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In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. We assume that the stock price process dynamics depends on an...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1608.07226
3
3.0
Jun 30, 2018
06/18
by
Tianyang Nie; Marek Rutkowski
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eye 3
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Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and Piterbarg (2010). Using the comparison theorems for BSDEs, we derive inequalities for the unilateral prices and we give the range for its fair bilateral prices. We also establish results yielding the link to the market model with a single interest rate. In the case...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1412.2453
9
9.0
Jun 30, 2018
06/18
by
Tomasz R. Bielecki; Marek Rutkowski
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eye 9
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The research presented in this work is motivated by recent papers by Brigo et al. (2011), Burgard and Kjaer (2009), Cr\'epey (2012), Fujii and Takahashi (2010), Piterbarg (2010) and Pallavicini et al. (2012). Our goal is to provide a sound theoretical underpinning for some results presented in these papers by developing a unified framework for the non-linear approach to hedging and pricing of OTC financial contracts. We introduce a systematic approach to valuation and hedging in nonlinear...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1405.4079
3
3.0
Jun 28, 2018
06/18
by
Robert Fernholz
texts
eye 3
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comment 0
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these markets are given: i) a market with a singular covariance matrix and instantaneous relative arbitrage; ii) a market with a singular covariance matrix and no arbitrage; iii) a market with a nonsingular covariance matrix and no arbitrage; iv) a market with a...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1512.02478
3
3.0
Jun 30, 2018
06/18
by
Samuel Drapeau; Peng Luo; Dewen Xiong
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eye 3
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comment 0
We characterize a class of fully coupled forward backward stochastic differential equations in terms of optimal maximal sub-solutions of BSDEs. We present the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We provide some explicit examples and show how to quantify the costs of incompleteness when using utility indifference pricing.
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1703.02694
10
10.0
Jun 28, 2018
06/18
by
Josselin Garnier; George Papanicolaou; Tzu-Wei Yang
texts
eye 10
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comment 0
We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force in the system. The local agents derive their stability only from the central agent. In the mean field limit of a large number of local agents we show that the systemic risk...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1507.08333
6
6.0
Jun 29, 2018
06/18
by
Carol Alexander; Johannes Rauch
texts
eye 6
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comment 0
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Hence there exist an infinite variety of other variance and higher-moment risk premia that are...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1602.00235
4
4.0
Jun 29, 2018
06/18
by
Philip Ernst; Larry Shepp
texts
eye 4
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comment 0
Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with martingales. Without martingale theory one could hardly prove our guess to be correct.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1605.00762
4
4.0
Jun 29, 2018
06/18
by
Vladimir Vovk; Glenn Shafer
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eye 4
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comment 0
This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain a simple expression for the equity premium and derive a version of the capital asset pricing model.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1607.00830
7
7.0
Jun 29, 2018
06/18
by
Birgit Rudloff
texts
eye 7
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comment 0
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1604.08070
4
4.0
Jun 29, 2018
06/18
by
Laurence Carassus; Romain Blanchard
texts
eye 4
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comment 0
This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1609.09205
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16
Jun 28, 2018
06/18
by
Simone Farinelli
texts
eye 16
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Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the "instantaneous arbitrage capability" generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1509.03264
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12
Jun 28, 2018
06/18
by
Xu Zuo Quan; Zhou Xun Yu; Zhuang Sheng Chao
texts
eye 12
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comment 0
Bernard et al. (2015) study an optimal insurance design problem where an individual's preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their contracts suffer from a problem of moral hazard for paying more compensation for a smaller loss. This paper addresses this setback by exogenously imposing the constraint that both the indemnity function and the insured's retention function be increasing with...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1509.04839
10
10.0
Jun 30, 2018
06/18
by
A. V. Lebedev; P. P. Zabreiko
texts
eye 10
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comment 0
The article presents a description of geometry of Banach structures forming mathematical base of markets arbitrage absence type phenomena. In this connection the role of reflexive subspaces (replacing classically considered finite-dimensional subspaces) and plasterable cones is uncovered.
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1410.4807
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12
Jun 26, 2018
06/18
by
Sergey Sosnovskiy
texts
eye 12
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comment 0
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametric Bayesian statistics, provides probabilistic-combinatorial approach for analysis and modeling of the capital distribution curve. Framework of the two-parameter Poisson-Dirichlet...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1501.01954
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22
Jun 26, 2018
06/18
by
Rohini Kumar
texts
eye 22
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In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1501.04548
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13
Jun 27, 2018
06/18
by
Tim Leung; Matthew Lorig
texts
eye 13
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We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1506.02074
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13
Jun 28, 2018
06/18
by
Ramin Okhrati; Uwe Schmock
texts
eye 13
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comment 0
Extending It\^o's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It\^o, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of It\^o's formula for diffusion processes where the Meyer-It\^o assumptions are weakened even further. We study a version of It\^o's formula for multi-dimensional finite variation L\'evy processes assuming that the...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1507.00294
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19
Jun 26, 2018
06/18
by
Yan Dolinsky; H. Mete Soner
texts
eye 19
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Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one the problems considered is the model--independent hedging that requires the super--replication to hold for every continuous path. In the second one the market model is given through a probability...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1502.01735
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15
Jun 27, 2018
06/18
by
Thai Huu Nguyen; Serguei Pergamenshchikov
texts
eye 15
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This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit theorems for the normalized replication error of Leland's strategy, as well as that of the strategy suggested by L\'epinette. The asymptotic results obtained not only generalize the existing results, but also enable us to fix the under-hedging property pointed out...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1505.02546
7
7.0
Jun 28, 2018
06/18
by
Ivan Degano; Sebastian Ferrando; Alfredo Gonzalez
texts
eye 7
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comment 0
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to take place at a finite number of occasions but not bounded in number nor necessarily equally spaced in time. For a given option, there exists an interval bounding the set of possible fair prices; such interval exists under more general conditions than the usual...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1511.01207
7
7.0
Jun 29, 2018
06/18
by
Christoph Czichowsky; Rémi Peyre; Walter Schachermayer; Junjian Yang
texts
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We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive answer for a continuous price process $S=(S_t)_{0\leq t\leq T}$ satisfying the condition $(NUPBR)$ of "no unbounded profit with bounded risk". This condition requires that $S$ is a semimartingale and therefore is too restrictive for applications to...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1608.01415
4
4.0
Jun 29, 2018
06/18
by
Thai Nguyen
texts
eye 4
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comment 0
This paper extends the results of the article [C. Kl\"{u}ppelberg and S. M. Pergamenchtchikov. Optimal consumption and investment with bounded downside risk for power utility functions. In Optimality and Risk: {\it Modern Trends in Mathematical Finance. The Kabanov Festschrift}, pages 133-169, 2009] to a jump-diffusion setting. We show that under the assumption that only positive jumps in the asset prices are allowed, the explicit optimal strategy can be found in the subset of admissible...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1604.05584
5
5.0
Jun 30, 2018
06/18
by
Xin Dong; Harry Zheng
texts
eye 5
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comment 0
In this paper we discuss a credit risk model with a pure jump L\'evy process for the asset value and an unobservable random barrier. The default time is the first time when the asset value falls below the barrier. Using the indistinguishability of the intensity process and the likelihood process, we prove the existence of the intensity process of the default time and find its explicit representation in terms of the distance between the asset value and its running minimal value. We apply the...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1405.3767
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13
Jun 29, 2018
06/18
by
Juan M. Romero; Ilse B. Zubieta-Martínez
texts
eye 13
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comment 0
Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale transformations. In this limit, we show that the stock prices distribution is given by a Cauchy distribution, instead of a normal distribution.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1604.01447
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8.0
Jun 29, 2018
06/18
by
Oliver Pfante; Nils Bertschinger
texts
eye 8
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comment 0
Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon's mutual information.
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1610.00312
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10.0
Jun 28, 2018
06/18
by
Nikolai Dokuchaev
texts
eye 10
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comment 0
We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stochastic integrals with respect to the Hurst parameter H at H=1/2.
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1509.06472
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6.0
Jun 28, 2018
06/18
by
Matteo Burzoni
texts
eye 6
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comment 0
We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage condition introduced in Schachermayer ['04] and show that this is equivalent to the existence of Consistent Price Systems. Moreover, we prove that the superhedging price for a claim g coincides with the frictionless superhedging price of g for a suitable process...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1512.01488
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14
Jun 29, 2018
06/18
by
Tim Leung; Jiao Li; Xin Li; Zheng Wang
texts
eye 14
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comment 0
This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential Ornstein-Uhlenbeck (XOU) model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the...
Topics: Mathematical Finance, Quantitative Finance
Source: http://arxiv.org/abs/1601.04210
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15
Jun 26, 2018
06/18
by
Karl Grosse-Erdmann; Fabien Heuwelyckx
texts
eye 15
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comment 0
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in particular, that the price in the discrete model tends to the price in the continuous Black-Scholes model. Our results are based on an asymptotic expansion of the binomial cumulative...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1502.02819
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17
Jun 27, 2018
06/18
by
Riccardo Fazio
texts
eye 17
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For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the option price field variable and the free boundary position, verify a prefixed error...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1504.04594
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10.0
Jun 27, 2018
06/18
by
Nikolai Dokuchaev
texts
eye 10
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We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market incompleteness is also non-robust. We show that, for any incomplete market from a wide class of discrete time models, there exists a complete market model with arbitrarily close...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1505.00638
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12
Jun 28, 2018
06/18
by
Kasper Larsen; Tanawit Sae Sue
texts
eye 12
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We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an application, we show that the equilibrium Sharpe ratio can be increased and the equilibrium interest rate can be decreased (simultaneously) when the investors' income streams...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1507.02974
3
3.0
Jun 30, 2018
06/18
by
K. Gad; J. L. Pedersen
texts
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The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American put. For each PDE the parameter may be interpreted as a rationality parameter of the holder of the option. The method may be extended to other valuation situations given as an...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1410.1287
3
3.0
Jun 30, 2018
06/18
by
Antoine E. Zambelli
texts
eye 3
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We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we explore whether it is possible to adjust the number of shares needed to effectively hedge our position to account for views on market dynamics from present until the end of our interval, to account for the time-dependence of the options' sensitivity to the...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1411.3947
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11
Jun 30, 2018
06/18
by
Giorgia Callegaro; Luciano Campi; Valeria Giusto; Tiziano Vargiolu
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In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer's utility indifference price of a given product in terms of continuous...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1407.7725
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4.0
Jun 30, 2018
06/18
by
David Hobson; Yeqi Zhu
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The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the risky assets (the endowed asset) are infinite, and transaction costs involving the other risky assets are zero. Effectively, the endowed asset can only be sold. In general, multi-asset optional consumption/optimal portfolio problems are very challenging, but...
Topics: Quantitative Finance, Mathematical Finance
Source: http://arxiv.org/abs/1409.8037
