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State Dependent Utility

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  • Jaime A. Londo\~no
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    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.

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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0603316.

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    Date of creation: Mar 2006
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    Handle: RePEc:arx:papers:math/0603316

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    1. Angelo Melino & Alan X. Yang, 2003. "State Dependent Preferences Can Explain the Equity Premium Puzzle," Working Papers melino-03-01, University of Toronto, Department of Economics.
    2. Campbell, John Y & Chacko, George & Rodriguez, Jorge & Viceira, Luis M, 2003. "Strategic Asset Allocation in a Continuous Time VAR Model," CEPR Discussion Papers, C.E.P.R. Discussion Papers 4160, C.E.P.R. Discussion Papers.
    3. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, Elsevier, vol. 52(1), pages 47-78, April.
    4. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Optimal consumption and portfolio rules with durability and habit formation," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(2-3), pages 525-550.
    5. Jaime A. Londo\~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    6. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Numerical analysis of a free-boundary singular control problem in financial economics," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(2-3), pages 297-327.
    7. Jean-Pierre Danthine & John B. Donaldson & Christos Giannikos & Hany Guirguis, 2004. "On the Consequences of State Dependent Preferences for the Pricing of Financial Assets," FAME Research Paper Series, International Center for Financial Asset Management and Engineering rp73, International Center for Financial Asset Management and Engineering.
    8. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
    9. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(8-9), pages 1377-1403, June.
    10. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 187-98, January.
    11. Jaime A. Londoño, 2003. "State Tameness: A New Approach for Credit Constrains," Finance, EconWPA 0305001, EconWPA, revised 16 Feb 2004.
    12. Dangl, Thomas & Wirl, Franz, 2004. "Investment under uncertainty: calculating the value function when the Bellman equation cannot be solved analytically," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(7), pages 1437-1460, April.
    13. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, Elsevier, vol. 49(1), pages 33-83, October.
    14. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 60(2), pages 428-438, August.
    15. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(11), pages 1841-1865, November.
    16. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 27(6), pages 971-986, April.
    17. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(2), pages 245-263, October.
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