-
作者：Ma, J; Zhang, JF
作者单位：Purdue University System; Purdue University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper we investigate a class of backward stochastic differential equations (BSDE) whose terminal values are allowed to depend on the history of a forward diffusion. We first establish a probabilistic representation for the spatial gradient of the viscosity solution to a quasilinear parabolic PDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BSDE. Such a representation then leads to a closed-form representation of the ma...
-
作者：Nagai, H; Peng, S
作者单位：University of Osaka; Shandong University
摘要：We consider an optimal investment problem for a factor model treated by Bielecki and Pliska (Appl. Math. Optim. 39 337-360) as a risk-sensitive stochastic control problem, where the mean returns of individual securities are explicitly affected by economic factors defined as Gaussian processes. We relax the measurability condition assumed as Bielecki and Pliska for the investment strategies to select. Our investment strategies are supposed to be chosen without using information of factor proces...
-
作者：Guasoni, P
作者单位：University of Pisa
摘要：We consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a no-arbitrage condition strictly weaker than the existence of a martingale measure, and when asset prices are quasi-left-continuous processes, we show the existence of optimal strategies. Applications include maximization of expected utility, minimization of coherent risk measures and hedging of contingent claims.
-
作者：Budhiraja, A
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：The classical results on the ergodic properties of the nonlinear filter previously have been proved under the crucial assumption that the signal process and the observation noise are independent. This assumption is quite restrictive and many important problems in engineering and stochastic control correspond to filtering models with correlated signal and noise. Unlike the case of independent signal and noise, the filter process in the general correlated case may not be Markov even if the signa...
-
作者：Fleming, WH; Sheu, SJ
作者单位：Brown University; Academia Sinica - Taiwan
摘要：We consider an optimal investment problem proposed by Bielecki and Pliska. The goal of the investment problem is to optimize the long-term growth of expected utility of wealth. We consider HARA utility functions with exponent -infinity < gamma < 1. The problem can be reformulated as an infinite time horizon risk-sensitive control problem. Some useful ideas and results from the theory of risk-sensitive control can be used in the analysis. Especially, we analyze the associated dynamical programm...
-
作者：Schmidli, H
作者单位：University of Copenhagen
摘要：We consider a classical risk model and allow investment into a risky asset modelled as a Black-Scholes model as well as (proportional) reinsurance. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation. We prove a verification theorem in order to show that any increasing solution to the HJB equation is bounded and solves the optimisation problem. We prove that an increasing solution to the HJB equation ...
-
作者：Antonelli, F; Kohatsu-Higa, A
作者单位：G d'Annunzio University of Chieti-Pescara; Pompeu Fabra University; Purdue University System; Purdue University
摘要：This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the McKean-Vlasov equation introduced by Bossy and Talay. More specifically, we consider approximations of the distribution and of the density of the solution of the stochastic differential equation associated to the McKean-Vlasov equation. The scheme adopted here is a mixed one: Euler-weakly interacting particle system. If n is the number of weakly interacting particles and h is the uniform s...
-
作者：Grote, MN; Speed, TP
作者单位：University of California System; University of California Davis; University of California System; University of California Berkeley
摘要：We derive a family of approximate sampling distributions for the symmetric overdominance model of population genetics. The distributions are selective versions of the Ewens Sampling Formula, which gives sample likelihoods under a model of neutral evolution. We draw on basic results for the general selection model of Ethier and Kurtz, and use mathematical tools well-suited for calculating expectations of symmetric functions of Poisson-Dirichlet atoms. We conclude by briefly examining a Human Le...
-
作者：Evans, SN; Steinsaltz, D
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called NK fitness landscapes. Inspired by spinglasses, these models have the attractive feature of being tunable, with regard to both overall size (through the parameter N) and connectivity (through K). There are N genes, each of which exists in two possible alleles [leading to a system indexed by {0, 1}(N)]; the fitness score of an allele at a given site is determined by the alleles of K neighbo...
-
作者：Filipovic, D; Zabczyk, J
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Polish Academy of Sciences
摘要：In this article we discuss Markovian term structure models in discrete time and with continuous state space. More precisely, we are concerned with the structural properties of such models if one has the Markov property for a part of the forward curve. We investigate the two cases where these parts are either a true subset of the forward curve, including the short rate, or the entire forward curve. For the former case we give a sufficient condition for the term structure model to be affine. For...
