Optimal Investment Strategy Based On C Onditional Entropic Risk Measure

In this paper,we research on optimal investment strategies to minimize investor 's risk in the stock market based on conditional entropic risk measure.In this paper,we introduce the following conditional entropic risk measure function when discussing the optimal investment strategy:?t?t(?)=1/?tlogE[e-?t?|Tt],?t>0.The parameter ?t varies with time.At this time,the risk measure does not have time consistency.First,we consider the investment strategy when the initial time t is fixed.We use backward stochastic differential equation(BSDE)to solve the problem and give the explicit solution of the optimal investment strategy.According to our definition,the result is verified.For the problem with no time consistency,we further study the local optimal problem of investment strategy.At the beginning,we assume the average earning ratio of stock ?u and the fluctuation ratio ?u are deterministic functions,and give the optimal investment strategy of the problem under this assumption.Then,we prove a verification theorem.We also discuss the case that there are several stocks in our investment strategy.At last,in the case that the fluctuation ratio ?u is uncertain,we give the optimal investment strategy of the PDE.