Utility maximization in an illiquid market

Abstract

We consider a stochastic optimization problem of maximizing the expected utility from terminal wealth in an illiquid market. A discrete time model is constructed with few additional state variables. The dynamic programming approach is then developed and used for numerical studies. No-arbitrage conditions were also discussed.

Keywords:

• liquidity risk
• limit order book
• price impact
• utility maximization
• dynamic programming

Keywords:

• 91B26
• 90C39
• 93E20
• 60H30

Acknowledgements

This research was partly supported by the European Research Council under the grant 228053-FiRM, Swiss Finance Institute and by the ETH Foundation.

Notes

^1. [email protected]

Additional information

Notes on contributors

H. Mete Soner

1 1. [email protected]