A Model of Optimal Consumption under Liquidity Risk with Random Trading Times

15 Pages Posted: 19 Sep 2008

See all articles by Huyên Pham

Huyên Pham

Université Paris VII Denis Diderot

Peter Tankov

Ecole Polytechnique, Paris

Abstract

We consider a portfolio/consumption choice problem in a market model with liquidity risk. The main feature is that the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous stochastic control problem, non-standard in the literature. The dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we provide a convergent numerical algorithm for the resolution to this coupled system of IDE. Several numerical experiments illustrate the impact of the restricted liquidity trading opportunities, and we measure in particular the utility loss with respect to the classical Merton consumption problem.

Suggested Citation

Pham, Huyen and Tankov, Peter, A Model of Optimal Consumption under Liquidity Risk with Random Trading Times. Mathematical Finance, Vol. 18, Issue 4, pp. 613-627, October 2008. Available at SSRN: https://ssrn.com/abstract=1270345 or http://dx.doi.org/10.1111/j.1467-9965.2008.00350.x

Huyen Pham (Contact Author)

Université Paris VII Denis Diderot ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205
France

Peter Tankov

Ecole Polytechnique, Paris ( email )

route de Saclay
Palaiseau, 91128
France

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