The optimal investment strategy under the disordered return and random inflation

Abstract

We mainly tackle the optimal portfolio problem when investors have partial information in the financial market, and the inflation risk is taken into account, the risky asset price is suddenly changed by impacts of major events which result in the asset return disorder at a random time. Applying semimartingale and backward stochastic differential equation theory, we deduce the optimal investment strategy and value process which satisfy the exponential utility maximization of terminal real wealth. Moreover, numerical simulations are presented to illustrate the effects of the expected inflation rate and inflation volatility on the optimal investment strategy, and to compare the asset return disorder with the normal situation.