Max-plus Stochastic Control and Risk-sensitivity Export

@article{citeulike:3937055, abstract = {In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to minimize the max-plus expectation of some max-plus additive running cost. Such problems arise naturally as limits of some types of risk sensitive stochastic control problems. The value function is a viscosity solution to a quasivariational inequality (QVI) of dynamic programming. Equivalence of this QVI to a nonlinear parabolic PDE with discontinuous Hamiltonian is used to prove a comparison theorem for viscosity sub- and super-solutions. An example from math finance is given, and an application in nonlinear H-infinity control is sketched.}, archivePrefix = {arXiv}, author = {Fleming, Wendell H. and Kaise, Hidehiro and Sheu, Shuenn-Jyi}, citeulike-article-id = {3937055}, citeulike-linkout-0 = {http://arxiv.org/abs/0901.3007}, citeulike-linkout-1 = {http://arxiv.org/pdf/0901.3007}, day = {20}, eprint = {0901.3007}, keywords = {control, tropical}, month = {Jan}, posted-at = {2009-01-25 08:39:14}, priority = {2}, title = {Max-plus Stochastic Control and Risk-sensitivity}, url = {http://arxiv.org/abs/0901.3007}, year = {2009} }

TY - JOUR ID - citeulike:3937055 L3 - citeulike-article-id:3937055 N2 - In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to minimize the max-plus expectation of some max-plus additive running cost. Such problems arise naturally as limits of some types of risk sensitive stochastic control problems. The value function is a viscosity solution to a quasivariational inequality (QVI) of dynamic programming. Equivalence of this QVI to a nonlinear parabolic PDE with discontinuous Hamiltonian is used to prove a comparison theorem for viscosity sub- and super-solutions. An example from math finance is given, and an application in nonlinear H-infinity control is sketched. TI - Max-plus Stochastic Control and Risk-sensitivity KW - control KW - tropical AU - Fleming, Wendell AU - Kaise, Hidehiro AU - Sheu, Shuenn-Jyi PY - 2009/Jan/20/ UR - http://arxiv.org/abs/0901.3007 ER -