Process-based risk measures and risk-averse control of discrete-time systems

摘要

For controlled discrete-time stochastic processes we introduce a new class ofdynamic risk measures, which we call process-based. Their main features arethat they measure risk of processes that are functions of the history of a baseprocess. We introduce a new concept of conditional stochastic time consistencyand we derive the structure of process-based risk measures enjoying thisproperty. We show that they can be equivalently represented by a collection ofstatic law-invariant risk measures on the space of functions of the state ofthe base process. We apply this result to controlled Markov processes and wederive dynamic programming equations.