Article2008

A MODEL OF OPTIMAL CONSUMPTION UNDER LIQUIDITY RISK WITH RANDOM TRADING TIMES

46 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

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.

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References

1971Optimum consumption and portfolio rules in a continuous-time model 1998Methods of Mathematical Finance 1990Portfolio Selection with Transaction Costs 1998Methods of Mathematical Finance 1993Markov Models & Optimization 1989Optimal replication of contingent claims under transaction costs 1995Martingales and Arbitrage in Securities Markets with Transaction Costs 2001A NONLINEAR FILTERING APPROACH TO VOLATILITY ESTIMATION WITH A VIEW TOWARDS HIGH FREQUENCY DATA

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2010Optimal Portfolio Liquidation with Execution Cost and Risk 2014Investment/Consumption Problem in Illiquid Markets with Regime-Switching 2010Optimal portfolios of a small investor in a limit order market: a shadow price approach

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