Optimal decision-making of mutual fund temporary borrowing problem via approximate dynamic programming

Abstract

Temporary borrowing is a liquidity risk management tool for mutual fund managers to meet investor redemption demands. We develop a new Markov decision process model to describe the temporary borrowing process, considering the multiple lending channels, the validity period of loans, and the uncertainties of cost, demand, and maximum loan amount simultaneously. An approximate dynamic programming (ADP) algorithm is initiated to solve the cost-minimizing temporary borrowing problem. We construct the value function as a separable approximation and prove the convexity of its components with respect to the available funds in different channels. Moreover, a new value function updating formula, DMAX, is designed to overcome value function overestimation. The proved convexity and the proposed formula contribute to fast and reliable value function estimation. Numerical experiments based on actual business data show that the proposed algorithm can obtain near-optimal decisions in deterministic cases and maintain high robustness in stochastic cases.