Risk-Sensitive Maximum Principle for Controlled System with Delay

Abstract

Risk-sensitive maximum principle and verification theorem for controlled system with delay is obtained by virtue of classical convex variational technique. The prime feature in the research is that risk-sensitive parameter ϑ seriously affects adjoint equation and variational inequality. Moreover, a verification theorem of optimality is derived under some concavity conditions. An example is given to illustrate our theoretical result.

Keywords

• maximum principle
• risk-sensitive optimal control
• stochastic differential equation with delay