Optimal Investment-consumption Strategies With Regime Switching Models Under CTE Constraints

In this paper,we consider the optimal investment-consumption strategies of regime switching models under CTE(also be known as CVaR)constraints.It is assumed that the price of risk asset obeys the Geometric Brownian Motion,and the volatility of risk asset depends on the state of economy.In the case of liabilities allowed,we focused on the utility function associated with consumptions and extended the results from the VaR constraints in the literature [1] to the CTE constraints,which provided a way to study the optimal investment portfolio to meet the regulatory agencies’ requirements on market risk control.The explicit expression of value function is obtained under certain conditions,and some defects in the literature [1] are corrected.In the case of liabilities not to be allowed,utility functions which combine investments and consumptions are discussed.This part not only makes our utility functions closer to reality,but also enriches the research and discussion of relevant models in the literature.This paper not only uses the dynamic programming principle,HJB equation,Lagrange multiplier method and other tools to obtain the conditions and equations for the optimal investment-consumption strategies under the CTE constraints,but also discusses the influence of multiple parameters on the optimal strategies by a numerical method with specific examples.