### Abstract

We consider the optimal investment and consumption problem in aBlack-Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!

Original language | English |
---|---|

Pages (from-to) | 21-40 |

Number of pages | 20 |

Journal | Mathematical Methods of Operations Research |

Volume | 74 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Aug 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Black-Scholes Market
- Risk aversion asymptotics
- Utility maximization

### ASJC Scopus subject areas

- Software
- Management Science and Operations Research
- Mathematics(all)

### Fields of Expertise

- Information, Communication & Computing

### Cite this

**Risk averse asymptotics in a Black-Scholes market on a finite time horizon.** / Grandits, Peter; Thonhauser, Stefan.

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

*Mathematical Methods of Operations Research*, vol. 74, no. 1, pp. 21-40. https://doi.org/10.1007/s00186-011-0347-4

}

TY - JOUR

T1 - Risk averse asymptotics in a Black-Scholes market on a finite time horizon

AU - Grandits, Peter

AU - Thonhauser, Stefan

PY - 2011/8/1

Y1 - 2011/8/1

N2 - We consider the optimal investment and consumption problem in aBlack-Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!

AB - We consider the optimal investment and consumption problem in aBlack-Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!

KW - Black-Scholes Market

KW - Risk aversion asymptotics

KW - Utility maximization

UR - http://www.scopus.com/inward/record.url?scp=80054940948&partnerID=8YFLogxK

U2 - 10.1007/s00186-011-0347-4

DO - 10.1007/s00186-011-0347-4

M3 - Article

VL - 74

SP - 21

EP - 40

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 1

ER -