Abstracts

We study the optimal portfolio problem of an investor who has the option to invest in an illiquid asset that is only traded at time 0. We use a generalized martingale method to solve the optimal investment problem and derive optimal strategies via Clark's formula and by introducing a liquidity derivative. As application, we study the optimal investment into a fixed-term deposit earning an excess return over the risk-free interest rate. We demonstrate that the presence of such an investment opportunity has a significant impact on optimum asset allocation: crra agents with realistic values of relative risk aversion can be expected to allocate more than 40\% of initial wealth to the illiquid investment opportunity if it yields an excess return of 100 basis points over the money market account. Furthermore, we look at an investor who gains utility by owning a housing good and solve the corresponding optimal investment problem in our setting.