Codice  QDD 177 
Titolo  Passive Portfolio Management over a Finite Horizon with a Target Liquidation Value under Transaction Costs and Solvency Constraints 
Data  20140422 
Autore/i  Baccarin, S.; Marazzina, D. 
Link  Download full text 
Abstract  We consider a passive investor who divides his capital between two assets: a riskfree money market instrument and an index fund, or ETF, tracking a broad market index. We model the evolution of the market index by a lognormal diffusion. The agent faces both fixed and proportional transaction costs and solvency constraints. The objective is to maximize the expected utility from the portfolio liquidation at a fixed horizon but if the portfolio reaches a preset target value then the position in the risky asset is liquidated. 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 quasivariational inequality. We show the existence of an impulse policy which is arbitrarily close to the optimal one by reducing the model to a sequence of iterated optimal stopping problems. The value function and the quasioptimal policy are computed numerically by an iterative finite element discretization technique. We present extended numerical results in the case of a CRRA utility function, showing the nonstationary shape of the optimal strategy and how it varies with respect to the model parameters. The numerical experiments reveal that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buyandhold trading strategy where the agent recalibrates his portfolio very few times. 
