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作者：Mansfield, P; Rachev, ST; Samorodnitsky, G
作者单位：University of Tasmania; Cornell University; Cornell University; Cornell University; Helmholtz Association; Karlsruhe Institute of Technology
摘要：We study long strange intervals in a linear stationary stochastic process with regularly varying tails. It turns out that the length of the longest strange interval grows, as a function of the sample size, at different rates in different parts of the parameter space. We argue that this phenomenon may be viewed in a fruitful way as a phase transition between short- and long-range dependence, We prove a limit theorem that may form a basis for statistical detection of long-range dependence.
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作者：Bank, P; Riedel, F
作者单位：Humboldt University of Berlin; Humboldt University of Berlin
摘要：We analyze the intertemporal utility maximization problem under uncertainty for the preferences proposed by Hindy, Huang and Kreps. Existence and uniqueness of optimal consumption plans are established under arbitrary convex portfolio constraints, including both complete and incomplete markets. For the complete market setting, we prove an infinite-dimensional version of the Kuhn-Tucker theorem which implies necessary and sufficient conditions for optimality. Using this characterization, we sho...
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作者：Khasminskii, RZ; Klebaner, FC
作者单位：Wayne State University; University of Melbourne
摘要：A stochastic analogue of the Lotka-Volterra model for predator-prey relationship is obtained when the birth rate of the prey and the death rate of the predator are perturbed by independent white noises with intensities of order epsilon (2), where epsilon > 0 is a small parameter. The evolution of this system is studied on large time intervals of O(1/epsilon (2)). It is shown that for small initial population sizes the stochastic model is adequate, whereas for large initial population sizes it ...
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作者：El Karoui, N; Peng, S; Quenez, MC
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Shandong University; Universite Gustave-Eiffel
摘要：This paper examines the continuous-time portfolio-consumption problem of an agent with a recursive utility in the presence of nonlinear constraints on the wealth. Using backward stochastic differential equations, we state a dynamic maximum principle which generalizes the characterization of optimal policies obtained by Duffie and Skiadas [J. Math Econ. 23, 107-131 (1994)] in the case of a linear wealth. From this property, we derive a characterization of optimal wealth and utility processes as...
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作者：Baryshnikov, Y; Gnedin, A
作者单位：Universite Paris Saclay; University of Gottingen
摘要：We consider a sequential interval packing process similar to Renyi's ''car parking problem'' but with a generator of random intervals which allows for arbitrarily small lengths. Embedding the process in continuous time, we view it as a self-similar interval splitting process. We determine the asymptotical behavior of the quantities such as the number of intervals packed to some instant and obtain convergence results in the context of the more general splitting model.
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作者：Berkes, I; Horváth, L
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Utah System of Higher Education; University of Utah
摘要：We obtain a strong approximation for the empirical process of n observed elements of a GARCH sequence. The weak convergence of the empirical process and the law of the iterated logarithm are immediate consequences.
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作者：Millet, A; Morien, PL
作者单位：Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Universite Paris Nanterre
摘要：In this paper, we investigate the existence and uniqueness of the solution for a class of stochastic wave equations in two space-dimensions containing a non-linearity of polynomial type. The method used in the proofs combines functional analysis arguments with probabilistic tools, and further estimates for the Green function associated with the classical wave equation.
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作者：Foley, RD; McDonald, DR
作者单位：University System of Georgia; Georgia Institute of Technology; University of Ottawa
摘要：We consider the stability of a network serving a patchwork of overlapping regions where customers from a local region are assigned to a collection of local servers. These customers join the queue of the local server with the shortest queue of waiting customers. We then describe how the backlog in the network overloads. We do this in the simple case of two servers each of which receives a dedicated stream of customers in addition to customers from a stream of smart customers who join the shorte...
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作者：Jankunas, A
摘要：Given a particular market variable, which could be finite dimensional (e.g., a price vector of a collection of stocks) or infinite dimensional (e.g., a price trajectory of some security over some period of time), we find the unique optimal European claim contingent on that variable in the sense that, for a given price and risk tolerance level, this claim has the highest expected return possible. The optimal contingent claims seem to be attractive investment instruments and are proposed for tra...
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作者：Schachermayer, W
作者单位：Technische Universitat Wien
摘要：This paper accompanies a previous one by D. Kramkov and the present author. While in [ 17] we considered utility functions U : R+ --> R satisfying the Inada conditions U'(0) = infinity and U'(infinity) = 0, in the present paper we consider utility functions U : R --> R which are finitely valued, for all x is an element of R, and satisfy U'(- infinity) = infinity and U'(infinity) = 0. A typical example of this situation is the exponential utility U(x) = -e(-x). In the setting of [17] the follow...
