Multi-Period Portfolio Optimization under Cash-In Strategies

Abstract

Portfolio optimization has been crucial in its applications to finance. Investors allocate capital in terms of various assets and wisely adjust each proportion in quest of higher returns and lower risks. However, common optimization strategies are usually short- sighted, lacking the ability of gaining higher returns over a long period. This paper addresses Multi-Period Portfolio Optimization problem in more applicable settings to provide efficient strategies. Firstly, a summary of conclusions from former works and scholars is given. Since most previous works assume self-financing conditions, this work extends this constraint and considers more complex cash-in and cash-out situations. It also derives the expression of the optimal policy for trading at each period as well as the objective functions. Finally, numerical experiments are done under both self-financing and cash-in situations to prove the validity of conclusions. This work has profound implications in finance because it adopts conditions more consistent with real-world scenarios and provides more farsighted strategies. Moreover, the solution offers a prototype for similar optimization in other fields like electrical engineering and stochastic processes.