Time Consistent Recursive Risk Measures Under Regime Switching and Factor Models and Their Application in Dynamic Portfolio Selection∗

The proper description of dynamic information correlation among individual stages is very important for the construction of multi-period risk measure and the selection of optimal investment strategy. To overcome the limitations of existing random frameworks, we initially introduce a ”two-level” structure to describe the dynamic information evolution: the outer-level describes endogenous marcomarket factors under the regime switching framework; the inner-level describes exogenous random events by the multi-factor model, where the time-varying factors are modeled by a time series model. Under the new random framework, we define the convex conditional risk measure and then derive the recursive multiperiod risk measure, which satisfies dynamic monotonicity, convexity and time consistency. We show how to establish the corresponding multi-stage portfolio selection model. Take the conditional value-at-risk (CVaR) measure as an example, we deduce the corresponding recursive CVaR measure and derive its explicit This research was supported by the National Natural Science Foundation of China (Grant Numbers 70971109 and 71371152). The corresponding author: [email protected] 1 expression when conditional factors and residual terms follow the joint student’s t distribution. More importantly, we show that the resulting multi-stage portfolio selection problems under the recursive CVaR measure are second-order cone programming, which can be efficiently solved in polynomial time. As a way to show the reasonability and efficiency of our new random framework, we carry out a series of empirical tests to demonstrate the superior performance and robustness of the optimal portfolio obtained with our multi-stage portfolio selection model. Keyword: Time consistency, recursive risk measure, regime switching, dynamic portfolio selection, conditional value-at-risk, factor model