Max-plus Stochastic Control and Risk-sensitivity

Details Max-plus Stochastic Control and Risk-sensitivity Max-plus Stochastic Control and Risk-sensitivity

2009-01-20

arxiv.org/abs/0901.3007v1

Mathematics

Optimization and Control

58 pages

Scientific paper

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.

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