Time consistency and time consistent generalized convex multistage risk measures.

After demonstrating four basic properties a multi-period risk measure should satisfy, a class of generalized convex multi-period risk measures is defined, which improves and extends existing coherent and convex multi-period risk measures. With respect to this kind of generalized convex multi-period risk measure, the equivalence among different notions of time consistency of risk measure is established. Furthermore, by introducing a fair property that any sophisticated multi-period risk measure should satisfy, we show that if the multi-period risk measure is time consistent, then optimal decisions derived under this risk measure also satisfy the time consistency of optimal policy. Finally, we present the concrete structure of the time consistent generalized convex multi-period risk measure, and illustrate through several examples how to construct time consistent generalized convex multi-period risk measures from existing single-period risk measures. [ABSTRACT FROM AUTHOR]