### Abstract

Mean-variance hedging is well-known as one of hedging methods for incomplete markets. Our end is leading to mean-variance hedging strategy for incomplete market models whose asset price process is given by a discontinuous semimartingale and whose mean-variance trade-off process is not deterministic. In this paper, on account, we focus on this problem under the following assumptions: (1) the local martingale part of the stock price process is a process with independent increments; (2) a certain condition restricting the number and the size of jumps of the asset price process is satisfied; (3) the mean-variance trade-off process is uniformly bounded; (4) the minimal martingale measure coincides with the variance-optimal martingale measure.

Original language | English |
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Pages (from-to) | 435-452 |

Number of pages | 18 |

Journal | Tokyo Journal of Mathematics |

Volume | 25 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Mean-Variance Hedging for Discontinuous Semimartingales.** / Arai, Takuji.

Research output: Contribution to journal › Article

*Tokyo Journal of Mathematics*, vol. 25, no. 2, pp. 435-452. https://doi.org/10.3836/tjm/1244208863

}

TY - JOUR

T1 - Mean-Variance Hedging for Discontinuous Semimartingales

AU - Arai, Takuji

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Mean-variance hedging is well-known as one of hedging methods for incomplete markets. Our end is leading to mean-variance hedging strategy for incomplete market models whose asset price process is given by a discontinuous semimartingale and whose mean-variance trade-off process is not deterministic. In this paper, on account, we focus on this problem under the following assumptions: (1) the local martingale part of the stock price process is a process with independent increments; (2) a certain condition restricting the number and the size of jumps of the asset price process is satisfied; (3) the mean-variance trade-off process is uniformly bounded; (4) the minimal martingale measure coincides with the variance-optimal martingale measure.

AB - Mean-variance hedging is well-known as one of hedging methods for incomplete markets. Our end is leading to mean-variance hedging strategy for incomplete market models whose asset price process is given by a discontinuous semimartingale and whose mean-variance trade-off process is not deterministic. In this paper, on account, we focus on this problem under the following assumptions: (1) the local martingale part of the stock price process is a process with independent increments; (2) a certain condition restricting the number and the size of jumps of the asset price process is satisfied; (3) the mean-variance trade-off process is uniformly bounded; (4) the minimal martingale measure coincides with the variance-optimal martingale measure.

UR - http://www.scopus.com/inward/record.url?scp=85035302554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035302554&partnerID=8YFLogxK

U2 - 10.3836/tjm/1244208863

DO - 10.3836/tjm/1244208863

M3 - Article

AN - SCOPUS:85035302554

VL - 25

SP - 435

EP - 452

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 2

ER -