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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]

This paper investigates a time consistent multiperiod mean-variance (MV) portfolio selection problem under the Markov regime-switching framework. We use a vector auto-regression model to forecast the values of market factors and then predict the returns of risky assets by using a regime-dependent linear multifactor model. By introducing the notion of separable expected conditional mapping, we construct a time consistent multiperiod MV model with regime switching. Under the self-financing constraint, we derive an analytical optimal investment policy satisfying time consistency and the corresponding MV efficient frontier by using dynamic programming. Empirical results are provided to illustrate the reasonability and practicality of the proposed new model and the derived explicit investment strategy. Especially, we find that the investor invests more in risky assets under a bull market than that under a consolidation market or a bear market; the MV efficient frontier under a bull market is much superior to those determined under a consolidation market and a bear market. [ABSTRACT FROM AUTHOR]