### Abstract

We deal with the problem of minimizing the probability of ruin of an insurer by optimal investment of parts of the surplus in the financial market, modeled by geometric Brownian motion. In a diffusion framework the classical solution to this problem is to hold a constant amount of money in stocks, which in practice means continuous adaption of the investment position. In this paper, we introduce both proportional and fixed transaction costs, which leads to a more realistic scenario. In mathematical terms, the problem is now of impulse control type. Its solution is characterized and calculated by iteration of associated optimal stopping problems. Finally some numerical examples illustrate the resulting optimal investment policy and its deviation from the optimal investment behaviour without transaction costs.

Original language | English |
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Pages (from-to) | 359-383 |

Number of pages | 25 |

Journal | European Actuarial Journal |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Dec 2013 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty

### Fields of Expertise

- Information, Communication & Computing

### Cite this

**Optimal investment under transaction costs for an insurer.** / Thonhauser, Stefan.

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

*European Actuarial Journal*, vol. 3, no. 2, pp. 359-383. https://doi.org/10.1007/s13385-013-0078-4

}

TY - JOUR

T1 - Optimal investment under transaction costs for an insurer

AU - Thonhauser, Stefan

PY - 2013/12/1

Y1 - 2013/12/1

N2 - We deal with the problem of minimizing the probability of ruin of an insurer by optimal investment of parts of the surplus in the financial market, modeled by geometric Brownian motion. In a diffusion framework the classical solution to this problem is to hold a constant amount of money in stocks, which in practice means continuous adaption of the investment position. In this paper, we introduce both proportional and fixed transaction costs, which leads to a more realistic scenario. In mathematical terms, the problem is now of impulse control type. Its solution is characterized and calculated by iteration of associated optimal stopping problems. Finally some numerical examples illustrate the resulting optimal investment policy and its deviation from the optimal investment behaviour without transaction costs.

AB - We deal with the problem of minimizing the probability of ruin of an insurer by optimal investment of parts of the surplus in the financial market, modeled by geometric Brownian motion. In a diffusion framework the classical solution to this problem is to hold a constant amount of money in stocks, which in practice means continuous adaption of the investment position. In this paper, we introduce both proportional and fixed transaction costs, which leads to a more realistic scenario. In mathematical terms, the problem is now of impulse control type. Its solution is characterized and calculated by iteration of associated optimal stopping problems. Finally some numerical examples illustrate the resulting optimal investment policy and its deviation from the optimal investment behaviour without transaction costs.

UR - http://www.scopus.com/inward/record.url?scp=84958690028&partnerID=8YFLogxK

U2 - 10.1007/s13385-013-0078-4

DO - 10.1007/s13385-013-0078-4

M3 - Article

VL - 3

SP - 359

EP - 383

JO - European actuarial journal

JF - European actuarial journal

SN - 2190-9733

IS - 2

ER -