Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints
We investigate a portfolio optimization problem for an agent who invests in two assets, a risk-free and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected utility from the portfolio liquidation at a terminal finite horizon. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We compute numerically the optimal policy by a an iterative finite element discretization technique, presenting extended numerical results in the case of a constant relative risk aversion utility function. Our results show that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times. This contrasts sharply with the continuous interventions of the Merton's model without transaction costs.
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- Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
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