2024/01/26 by Wenyuan Wang, Kaixin Yan, Wang, Wenyuan +3
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #Monetary Policy and Economic Impact #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.14672
openalex publication_date 2024/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon. For both power and logarithmic utilities, we formulate the auxiliary one-period optimization problems with modified utility functions, for which we develop the martingale duality approach to establish the existence of the optimal portfolio processes and the dual minimizers can be identified as the "least favorable" completion of the market. With the help of the duality results in the auxiliary problems and some fixed point arguments, we further derive and verify the optimal portfolio processes in a periodic manner for the original periodic evaluation problems over an infinite horizon.