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An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations

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  • Xiang Yu
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    Abstract

    We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only observing the market stock prices but not the instantaneous rate of return. Applying the Kalman-Bucy filtering theorem and the Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equation explicitly for the path dependent stochastic control problem in the case of power utilities. We provide the optimal investment and consumption policies in explicit feedback forms using rigorous verification arguments.

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    File URL: http://arxiv.org/pdf/1112.2939
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1112.2939.

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    Date of creation: Dec 2011
    Date of revision: Aug 2014
    Handle: RePEc:arx:papers:1112.2939

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    1. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(11), pages 3560-3589, November.
    2. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 15(2), pages 145-161, March.
    3. 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.
    4. Mark Schroder & Costis Skiadas, 2002. "An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 15(4), pages 1189-1221.
    5. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 76(1), pages 77-97, August.
    6. Jerome B. Detemple & Fernando Zapatero, 1992. "Optimal Consumption-Portfolio Policies With Habit Formation," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 2(4), pages 251-274.
    7. Björk, Tomas & Davis, Mark H.A. & Landén, Camilla, 2010. "Optimal Investment under Partial Information," Working Paper Series in Economics and Finance 739, Stockholm School of Economics.
    8. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 116(5), pages 701-723, May.
    9. Detemple, Jerome B & Zapatero, Fernando, 1991. "Asset Prices in an Exchange Economy with Habit Formation," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1633-57, November.
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