Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino in its series Working papers with number 017.
Length: 35 pages
Date of creation: Jan 2013
Date of revision:
Portfolio Optimization; Quasi-variational Inequalities; Transaction Costs; Viscosity Solutions;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-02-03 (All new papers)
- NEP-CMP-2013-02-03 (Computational Economics)
- NEP-ORE-2013-02-03 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
- 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.
- Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
- Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long-Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188.
- Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
- Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335.
- Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Pellegrino).
If references are entirely missing, you can add them using this form.