Optimal Expected Utility From Terminal Wealth Under Liquidity Risk

We consider a portfolio problem in a market model with liquidity risk. The mainfeature is that there is no inaccessible jumps in this financial market model and theinvestor can only trade stocks in in fixed times. Hence, our main aim is how to choose anoptimal portfolio that can maximize the expected utility from terminal wealth. In thispaper, we introduce a classical utility function, under which we study the optimalinvesting strategy.Huyên Pham and Peter Tankov (2009)[9]studied optimal consumption policies inilliquid market, Michael Kohlmann and Dewen Xiong (2007)[18]considered-optimalmartingale measure in an incomplete financial market model with inaccessible jumps andwithout liquidity risk, they obtained the optimal investing policy which will realize theexpected utility from terminal wealth with a utility function.Similar to Michael Kohlmann and Dewen Xiong (2007)[18], we first introduce a newmartingale measure as the basic underlying measure. By using the dynamicprogramming principle, we establish a backward martingale equation (BME), and proveda theorem that the BME has a solution, if and only if there exists a change of measurethat the terminal wealth process can be expressed with the Radon-Nikodym derivative.Finally, we can obtain the optimal investing strategy and the optimal terminal wealthprocess using the solution of the BME.