Risk sensitive optimal control and differential games

Risk-sensitive stochastic control problems for nonlinear systems described by stochastic differential equations are considered. A logarithmic transformation is applied to the optimal cost function. The value function for a zero-sum, two-controller differential game is obtained in the limit, as a small parameter which represents noise intensity tends to zero. Convergence to the value function is proved by viscosity solution methods for nonlinear partial differential equations.

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