Optimal Investment with Quadratic Transaction Costs in a Multi-factor and Stochastic Interest Rate Environment (with Lingfei Li and Qianyu Liu).
+ Working Paper. [Abstract|SSRN]
+
+
+ This paper studies an optimal investment problem in a comprehensive market environment featuring geometric Brownian motion type asset dynamics, stochastic interest rates, return and volatility factors, and time-varying, state-dependent quadratic transaction costs. Under a finite-horizon mean-quadratic variation objective, we derive a semi-analytical solution for the value function and optimal trading strategy and establish the well-posedness of the associated system of nonlinear PDEs along with the verification theorem. The optimal strategy retains a tractable structure that echoes the core economic principle of trading gradually toward an aim portfolio as proposed in Gârleanu and Pedersen (2013). Specifically, the aim portfolio is adjusted for hedging demands against the interest rate risk, and the trading speed reflects an intertemporal trade-off between immediate rebalancing costs and future market liquidity. Additionally, we propose a deep learning scheme to enable efficient implementation in high-dimensional settings based on observable market data and estimated factor models.
+
+