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作者：Jarrow, Robert A.; Protter, Philip; Sayit, Hasanjan
作者单位：Cornell University; Cornell University; Worcester Polytechnic Institute
摘要：We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.
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作者：Craddock, Mark; Lennox, Kelly A.
作者单位：University of Technology Sydney
摘要：This paper uses Lie symmetry methods to calculate certain expectations for a large class of Ito diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form E-x(e(-lambda Xt-f0tg(Xs)ds)) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for whic...
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作者：Garnier, Josselin; Solna, Knut
作者单位：Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; University of California System; University of California Irvine
摘要：In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schrodinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation ...
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作者：Zitkovic, Gordan
作者单位：University of Texas System; University of Texas Austin
摘要：We propose a mathematical framework for the study of a family of random fields-called forward performances-which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the or...
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作者：Ekstrom, Erik; Tysk, Johan
作者单位：Uppsala University
摘要：A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black-Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show tha...
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作者：Buchmann, Boris; Chan, Ngai Hang
作者单位：Monash University; Chinese University of Hong Kong
摘要：Consider Z(t)(f) (u) = integral o(tu) f (N(s)) ds, t > 0, u is an element of [0, 1], where N = (N(t))t is an element of R is a normal process and f is a measurable real-valued function satisfying Ef(N(0))(2) < infinity and Ef (N(0)) = 0. If the dependence is sufficiently weak Hariz [J. Multivariate Anal. 80 (2002) 191-216] showed that Z(t)(f)/t(1/2) converges in distribution to a multiple of standard Brownian motion as t -> infinity. If the dependence is sufficiently strong, then Zt/(EZ(t) (1)...
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作者：D'Angeli, Daniele; Donno, Alfredo
作者单位：University of Geneva
摘要：In this work we define two kinds of crested product for reversible Markov chains, which naturally appear as a generalization of the case of crossed and nested product, as in association schemes theory, even if we do a construction that seems to be more general and simple. Although the crossed and nested product are inspired by the study of Gelfand pairs associated with the direct and the wreath product of two groups, the crested products are a more general construction, independent from the Ge...
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作者：Walton, N. S.
作者单位：University of Cambridge
摘要：We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that...
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作者：Hofbauer, Josef; Imhof, Lorens A.
作者单位：University of Vienna; University of Bonn; University of Bonn
摘要：We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure...
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作者：Tanaka, Hideyuki; Kohatsu-Higa, Arturo
作者单位：Mitsubishi International Corporation (MIC); University of Osaka
摘要：Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a general framework based on semigroup expansions for the construction of higher-order discretization schemes and analyze its rate of convergence. We also apply it to approximate general Levy driven stochastic differential equations.
