Utility maximization in an illiquid market in continuous time

H. Mete Soner; Mirjana Vukelja

doi:10.1007/s00186-016-0544-2

Utility maximization in an illiquid market in continuous time

H. Mete Soner, Mirjana Vukelja

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the unique discontinuous viscosity solution. This characterization is utilized to obtain numerical results for the optimal strategy and the loss due to illiquidity.

Original language	English (US)
Pages (from-to)	285-321
Number of pages	37
Journal	Mathematical Methods of Operations Research
Volume	84
Issue number	2
DOIs	https://doi.org/10.1007/s00186-016-0544-2
State	Published - Oct 1 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
General Mathematics
Management Science and Operations Research

Keywords

Comparison theorem
Hamilton–Jacobi–Bellman equation
Liquidity risk
Price impact
Viscosity solution
Weak dynamic programming

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10.1007/s00186-016-0544-2

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abstract = "A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the unique discontinuous viscosity solution. This characterization is utilized to obtain numerical results for the optimal strategy and the loss due to illiquidity.",

keywords = "Comparison theorem, Hamilton–Jacobi–Bellman equation, Liquidity risk, Price impact, Viscosity solution, Weak dynamic programming",

author = "Soner, {H. Mete} and Mirjana Vukelja",

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N2 - A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the unique discontinuous viscosity solution. This characterization is utilized to obtain numerical results for the optimal strategy and the loss due to illiquidity.

AB - A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the unique discontinuous viscosity solution. This characterization is utilized to obtain numerical results for the optimal strategy and the loss due to illiquidity.

KW - Comparison theorem

KW - Hamilton–Jacobi–Bellman equation

KW - Liquidity risk

KW - Price impact

KW - Viscosity solution

KW - Weak dynamic programming

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JO - Mathematical Methods of Operations Research

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ER -

Utility maximization in an illiquid market in continuous time

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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