Max-Plus Stochastic Control and Risk-Sensitivity

Max-Plus Stochastic Control and Risk-Sensitivity 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 mathematical finance is given, and an application in nonlinear H -infinity control is sketched. Applied Mathematics and Optimization Springer Journals

Max-Plus Stochastic Control and Risk-Sensitivity

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Copyright © 2010 by Springer Science+Business Media, LLC
Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
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