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作者：Deaconu, Madalina; Lejay, Antoine
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation ...
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作者：Barral, Julien; Jin, Xiong; Mandelbrot, Benoit
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Inria; Yale University
摘要：Positive T-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We focus on martingales constructed on the interval T = [0, 1] and replace random measures by random functions. We specify a large class of such martingales for which we provide a general sufficient condition for almost sure uniform convergence to a nontrivial li...
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作者：Barral, Julien; Jin, Xiong; Mandelbrot, Benoit
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Inria; Yale University
摘要：The familiar cascade measures are sequences of random positive measures obtained on [0, 1] via b-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values. This yields sequences of random functions whose possible strong or weak limits are natural candidates for modeling multifractal phenomena. Their asymptotic behavior is investigated, yielding a sufficient condition for almost sure uniform convergence to nontrivi...
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作者：Mertikopoulos, Panayotis; Moustakas, Aris L.
作者单位：National & Kapodistrian University of Athens
摘要：We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the aggregate shocks approach of evolutionary game theory. Irrespective of the perturbations' magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game's...
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作者：Fernholz, Daniel; Karatzas, Ioannis
作者单位：University of Texas System; University of Texas Austin
摘要：In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of the covariance structure of the model. The solution is intimately related to properties of strict local martingales and is used to generate the investment strategy which realizes t...
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Northwestern University
摘要：We consider a process X(t), which is observed on a finite time interval [0, T], at discrete times 0, Delta(n), 2 Delta(n), ... . This process is an Ito semimartingale with stochastic volatility sigma(2)(t). Assuming that X has jumps on [0, T], we derive tests to decide whether the volatility process has jumps occurring simultaneously with the jumps of X(t). There are two different families of tests for the two possible null hypotheses (common jumps or disjoint jumps). They have a prescribed as...
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作者：Alon, Noga; Gurel-Gurevich, Ori; Lubetzky, Eyal
作者单位：Tel Aviv University; Microsoft; MICROSOFT ISRAEL; Microsoft
摘要：In the classical balls-and-bins paradigm, where n balls are placed independently and uniformly in n bins, typically the number of bins with at least two balls in them is Theta(n) and the maximum number of balls in a bin is Theta(log n/log log n). It is well known that when each round offers k independent uniform options for bins, it is possible to typically achieve a constant maximal load if and only if k = Omega (log n). Moreover, it is possible w.h.p. to avoid any collisions between n/2 ball...
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作者：Azcue, Pablo; Muler, Nora
作者单位：Universidad Torcuato Di Tella
摘要：We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramer-Lundberg process. The firm has the option of investing part of the surplus in a Black-Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the...
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作者：James, Lancelot F.
作者单位：Hong Kong University of Science & Technology
摘要：This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an alpha-stable law, for 0 < alpha < 1, and the other variable has the law defined by polynomially tilting the density of an alpha-stable random variable by a factor theta > -alpha. When theta = 0, these variables equate with the ratio investigated by Lamperti [Trans. Amer. Math. Soc. 88 (1958) 380-387] which, remarkably, was shown to h...
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作者：Delong, Lukasz; Imkeller, Peter
作者单位：Warsaw School of Economics; Humboldt University of Berlin
摘要：We deal with backward stochastic differential equations with time delayed generators. In this new type of equation, a generator at time t can depend on the values of a solution in the past, weighted with a time delay function, for instance, of the moving average type. We prove existence and uniqueness of a solution for a sufficiently small time horizon or for a sufficiently small Lipschitz constant of a generator. We give examples of BSDE with time delayed generators that have multiple solutio...
