A Kind of Optimal Investment Problem under Inflation and Uncertain Exit Time

This paper is concerned with a kind of optimal portfolio choice problem, in which an investor can invest his wealth either in a bank account or in an real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. We take inflation and uncertain exit time into consideration and transform it into a control problem. For deterministic market parameters case, we employ dynamic programming principle to obtain the optimal strategy. For stochastic case, we get a explicit solution by the solution of two stochastic Riccati equations (SREs) for constant relative risk aversion (CRRA) case. Moreover, we present several numerical examples to show the application of theoretical results and further discuss the influence of inflation and uncertain exit time.