### Abstract

In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger's order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.

Original language | English |
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Pages (from-to) | 29-53 |

Number of pages | 25 |

Journal | Review of Derivatives Research |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Finance
- Economics, Econometrics and Finance (miscellaneous)

### Cite this

**Dynamic programming and mean-variance hedging with partial execution risk.** / Matsumoto, Koichi.

Research output: Contribution to journal › Article

*Review of Derivatives Research*, vol. 12, no. 1, pp. 29-53. https://doi.org/10.1007/s11147-009-9033-6

}

TY - JOUR

T1 - Dynamic programming and mean-variance hedging with partial execution risk

AU - Matsumoto, Koichi

PY - 2009/4/1

Y1 - 2009/4/1

N2 - In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger's order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.

AB - In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger's order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.

UR - http://www.scopus.com/inward/record.url?scp=67349267303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349267303&partnerID=8YFLogxK

U2 - 10.1007/s11147-009-9033-6

DO - 10.1007/s11147-009-9033-6

M3 - Article

AN - SCOPUS:67349267303

VL - 12

SP - 29

EP - 53

JO - Review of Derivatives Research

JF - Review of Derivatives Research

SN - 1380-6645

IS - 1

ER -