Abstract
We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).
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Nutz, M. Risk aversion asymptotics for power utility maximization. Probab. Theory Relat. Fields 152, 703–749 (2012). https://doi.org/10.1007/s00440-010-0334-3
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DOI: https://doi.org/10.1007/s00440-010-0334-3
Keywords
- Power utility
- Risk aversion asymptotics
- Opportunity process
- BSDE
Mathematics Subject Classification (2000)
- Primary 91B28
- Secondary 93E20
- 60G44