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# State Dependent Utility

## Author

Listed:
• Jaime A. Londo~no

## Abstract

We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is one proposed by the author in Dynamic State Tameness {arXiv:math.PR/0509139}. The proposed framework is a generalization of the theory of Brownian flows and can be applied to those processes that are the solutions of classical It^o stochastic differential equations, even when the volatilities and drifts are just locally $\delta$-Holder continuous for some $\delta>0$. We develop the martingale methodology for the solution of the problem of optimal consumption and investment. Complete solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities in the current literature, and consider general restrictions on minimal wealths. As a secondary result we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies.

## Suggested Citation

• Jaime A. Londo~no, 2006. "State Dependent Utility," Papers math/0603316, arXiv.org.
• Handle: RePEc:arx:papers:math/0603316
as

File URL: http://arxiv.org/pdf/math/0603316

## References listed on IDEAS

as
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13. Jaime A. Londoño, 2003. "State Tameness: A New Approach for Credit Constrains," Finance 0305001, University Library of Munich, Germany, revised 16 Feb 2004.
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18. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-198, January.
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20. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
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