Relaxed utility maximization in complete markets. (English) Zbl 1252.91076

For a relaxed investor whose relative risk aversion vanishes as wealth becomes large the utility maximization problem may not have a solution in the classical sense of the optimal payoff represented by a random variable. This was discovered by D. Kramkov and W. Schachermayer [Ann. Appl. Probab. 9, No. 3, 904–950 (1999; Zbl 0967.91017)] who introduced an asymptotic elasticity condition to exclude such situations. This paper decomposes relaxed expected utility into its classical and singular parts, represents the singular part in integral form, and proves the existence of optimal solutions for the utility maximization problem without conditions on the asymptotic elasticity.


91G20 Derivative securities (option pricing, hedging, etc.)
91G10 Portfolio theory


Zbl 0967.91017
Full Text: DOI


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