Max-plus Stochastic Control and Risk-sensitivity
| dc.creator | Fleming, Wendell H. | |
| dc.creator | Kaise, Hidehiro | |
| dc.creator | Sheu, Shuenn-Jyi | |
| dc.date | 2009-01-20 | |
| dc.date.accessioned | 2026-07-07T12:32:08Z | |
| dc.date.available | 2026-07-07T12:32:08Z | |
| dc.description | 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. | |
| dc.description | 58 pages | |
| dc.identifier | https://arxiv.org/abs/0901.3007 | |
| dc.identifier | http://arxiv.org/abs/0901.3007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216682 | |
| dc.subject | Optimization and Control | |
| dc.subject | Probability | |
| dc.subject | 35F20 (Primary) 49L20, 49L25, 93E03 (Secondary) | |
| dc.title | Max-plus Stochastic Control and Risk-sensitivity | |
| dc.type | text |