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作者：Kramkov, Dmitry; Pulido, Sergio
作者单位：Carnegie Mellon University; Universite Paris Saclay; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best ...
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作者：Sabanis, Sotirios
作者单位：University of Edinburgh
摘要：A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these explicit schemes converge in probability and in L-P to the solution of the corresponding SDEs. Moreover, rate of convergence estimates are provided for L-P and almost sure convergence. In particular, the strong order 1/2 is recovered in the case of uniform L...
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作者：Beskos, Alexandros; Jasra, Ajay; Kantas, Nikolas; Thiery, Alexandre
作者单位：University of London; University College London; National University of Singapore; Imperial College London
摘要：In several implementations of Sequential Monte Carlo (SMC) methods it is natural and important, in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In this article we provide a carefully formulated asymptotic theory for a class of such adaptive SMC methods. The theoretical framework developed here will cover, under assumptions, several commonly used SMC algorithms [Chopin, Biometrika 89 (2002) 539-551; Ja...
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作者：Takahashi, Akihiko; Yamada, Toshihiro
作者单位：University of Tokyo; Mitsubishi International Corporation (MIC)
摘要：This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion with multidimensional Malliavin weights to compute a target expectation value precisely. The mathematical validity is given based on Watanabe and Kusuoka theories in Malliavin calculus. Moreover, numerical experiments for option pricing under local and ...
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作者：Costa, Manon
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We are interested in prey-predator communities where the predator population evolves much faster than the prey's (e.g., insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that it is exponentially ergodic. Further on, we rescale the predator dynamics in order to model predator...
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作者：Penrose, Mathew D.
作者单位：University of Bath
摘要：Consider a graph on n uniform random points in the unit square, each pair being connected by an edge with probability p if the inter-point distance is at most r. We show that as n -> infinity the probability of full connectivity is governed by that of having no isolated vertices, itself governed by a Poisson approximation for the number of isolated vertices, uniformly over all choices of p, r. We determine the asymptotic probability of connectivity for all (p(n), r(n)) subject to r(n) = o(n(-e...
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作者：Kelly, David
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and MCMC algorithms. We make no particular probabilistic assumptions on the type of noise appearing in these recursions. Thus, our technique is well suited to recursions where the noise sequence is not a semi-martingale, even though the limiting noise may be. Our m...
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作者：Benaim, Michel; Lobry, Claude
作者单位：University of Neuchatel; Universite Cote d'Azur
摘要：We consider two-dimensional Lotka-Volterra systems in a fluctuating environment. Relying on recent results on stochastic persistence and piece wise deterministic Markov processes, we show that random switching between two environments that are both favorable to the same species can lead to the extinction of this species or coexistence of the two competing species.
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作者：Broutin, Nicolas; Devroye, Luc; Lugosi, Gabor
作者单位：McGill University; Pompeu Fabra University
摘要：A random geometric irrigation graph Gamma(n)(r(n), xi) has n vertices identified by n independent uniformly distributed points X-1, ..., X-n in the unit square [0, 11(2). Each point X-i selects xi(i) neighbors at random, without replacement, among those points X-i (j not equal i) for which parallel to X-i - X-j parallel to < r(n), and the selected vertices are connected to X-i by an edge. The number xi(i) of the neighbors is an integer-valued random variable, chosen independently with identica...
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作者：Carmona, Rene; Zhu, Xiuneng
作者单位：Princeton University
摘要：We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over conditional McKean-Vlasov stochastic differential equations. The definition of this limiting game is justified by proving that its solution provides approximate Nash equilibriums for large finite player games. This proof depends upon the generalization of sta...
