Articlebronze2006

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

97 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 study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.

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References

1988Liquidity and Market Structure 1999The asymptotic elasticity of utility functions and optimal investment in incomplete markets 1989Optimal replication of contingent claims under transaction costs 2004Liquidity risk and arbitrage pricing theory 2010Liquidity Risk and Arbitrage Pricing Theory 2003Hedging and Portfolio Optimization in Financial Markets with a Large Trader 1996Hedging options for a large investor and forward-backward SDE's 1997Market Volatility and Feedback Effects from Dynamic Hedging

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2010Hedging of Claims with Physical Delivery under Convex Transaction Costs 2011RESILIENT PRICE IMPACT OF TRADING AND THE COST OF ILLIQUIDITY 2011Liquidity risk, price impacts and the replication problem 2015OPTION PRICING AND HEDGING WITH EXECUTION COSTS AND MARKET IMPACT 2012Duality and convergence for binomial markets with friction 2011Liquidity Models in Continuous and Discrete Time

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