Title
Periodic Evaluation with Non-Concave Utility
Abstract
A fund manager’s performance is often evaluated annually and compared with a benchmark, such as a market index. In addition, the manager may be subject to trading constraints, such as limited use of leverage, no short-selling, and a forced liquidation clause. We formulate this as a periodic evaluation problem with a non-concave utility, a stochastic reference point, and trading constraints. The value function is characterized as the unique solution to a Hamilton-Jacobi-Bellman equation with periodic terminal and boundary conditions, which must be imposed carefully due to possible discontinuities at the terminal time and/or on the liquidation boundary. We find that, at the evaluation time, future investment opportunities induce a discontinuity in the value function on the liquidation boundary, leading to a substantial change in local risk-aversion. More importantly, this local concavity/convexity weakens and shifts inward from the liquidation boundary to the interior region as the evaluation horizon increases. As a result, the joint effect of periodic evaluation and forced liquidation can generate highly nonlinear investment strategies, which is helpful in understanding the complexity of trading strategies in the loss region.
Bio
Dr. Cong Qin is an Assistant Professor at the School of Finance, Shanghai University of Finance and Economics (SUFE). Before joining SUFE, he was an Associate Professor at the Center for Financial Engineering, Soochow University. His research focuses on financial engineering, fintech, and behavioral finance. His work has been published or accepted in top-tier finance journals such as the Journal of Finance, leading financial engineering journals like Mathematical Finance and SIAM Journal on Financial Mathematics, among others.