Max-Plus Stochastic Control and Risk-Sensitivity

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-010-9097-6· OSTI ID:21480260

Kaise, Hidehiro ^[1]; Sheu, Shuenn-Jyi ^[2]

---

1. Nagoya University, Graduate School of Information Science (Japan)
2. Academia Sinica, Institute of Mathematics (China)

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.

• OSTI ID: 21480260
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 62; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CALCULATION METHODS
COMPARATIVE EVALUATIONS
CONTROL THEORY
DIFFERENTIAL EQUATIONS
DYNAMIC PROGRAMMING
EQUATIONS
EVALUATION
FUNCTIONS
HAMILTONIANS
HAZARDS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM OPERATORS
RANDOMNESS
SCALARS
SENSITIVITY
STOCHASTIC PROCESSES