Dynamic asset-liability management with frictions

This paper studies a dynamic asset-liability management problem of a company with market frictions. Specifically, the asset prices are modeled by a multivariate geometric Brownian motion with their excess returns driven by some correlated stochastic signals; and the liability process is modeled by another geometric Brownian motion correlated to the asset price dynamics. The company trades dynamically to offset the risks from its liability and each trade induces both temporary and persistent price impacts. We characterize the optimal trading strategies in terms of the solutions to the coupled matrix Riccati differential systems. Due to the price impacts, the company should adopt a target-chasing strategy in which the dynamic target portfolio is expressed in terms of the return-predicting signals and realized liability. We also derive some sufficient conditions, based on the model parameters alone, to ensure the well-posedness of the coupled Riccati systems. Our numerical results indicate that the temporary and persistent price impacts have opposite implications on the company's trading behavior. While the temporary price impact slows down the company's trading speed toward the target portfolio, the persistent price impact may encourage the company to trade more aggressively to enhance the expected returns.