2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216682In 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.58 pagesOptimization and ControlProbability35F20 (Primary) 49L20, 49L25, 93E03 (Secondary)text