Multiple objective risk-sensitive control and stochastic differential games

Abstract

In this paper, we study a (minimizing) multiple-objective risk-sensitive control problem, and show the relationship between this problem, a certain stochastic differential game, and what may be regarded as a multiple-objective deterministic differential game. The limiting deterministic differential game is one in which the opponent seeks to maximize the most vulnerable member of a set of given cost functionals, while the original controller seeks to minimize the worst 'damage' that the opponent can do over this set. This forms a natural framework in which many applications can be studied.