Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints

Stefano Baccarin () and Daniele Marazzina ()
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Stefano Baccarin: Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy
Daniele Marazzina: Department of Mathematics, Polytechnic University of Milano, Italy

No 17, Working papers from Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino

Abstract: 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.

Keywords: Portfolio Optimization; Quasi-variational Inequalities; Transaction Costs; Viscosity Solutions (search for similar items in EconPapers)
JEL-codes: C61 D92 G11 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2013-01
New Economics Papers: this item is included in nep-cmp and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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http://www.bemservizi.unito.it/repec/tur/wpapnw/m17.pdf First version, 2013 (application/pdf)

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