Mathematical Methods of Operations Research

, Volume 74, Issue 1, pp 21–40 | Cite as

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

  • Peter Grandits
  • Stefan ThonhauserEmail author
Original Article


We consider the optimal investment and consumption problem in a Black–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!


Utility maximization Risk aversion asymptotics Black–Scholes market 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institute for Mathematical Methods in EconomicsTU ViennaViennaAustria
  2. 2.Institute of Actuarial ScienceUniversity of LausanneLausanneSwitzerland

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