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

Peter Grandits, Stefan Thonhauser

Research output: Contribution to journalArticleResearchpeer-review

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 languageEnglish
Pages (from-to)21-40
Number of pages20
JournalMathematical Methods of Operations Research
Volume74
Issue number1
DOIs
Publication statusPublished - 1 Aug 2011
Externally publishedYes

Fingerprint

Black-Scholes
Horizon
Expected Utility
Optimal Investment
Risk Aversion
Relative Risk
Optimal Strategy
Stock Market
Limiting
Infinity
Tend
Target
Market
Discounted utility
Time horizon
Risk-averse
Financial markets
Wealth
Optimal investment
Optimal consumption

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.

In: Mathematical Methods of Operations Research, Vol. 74, No. 1, 01.08.2011, p. 21-40.

Research output: Contribution to journalArticleResearchpeer-review

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