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Time-Inconsistent Mean-Utility Portfolio Selection with Moving Target

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  • Hanqing Jin
  • Yimin Yang
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    Abstract

    In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our optimal control. We firstly derive a sufficient equilibrium condition for second-order continuously differentiable utility funtions. Then we use power functions of order two, three and four in our problem and find the respective condtions for obtaining an equilibrium for our different problems. In the last part of the paper, we consider using another definition of equilibrium to solve our problem when the utility function that we use in our problem is the negative part of x and also find the condtions for obtaining an equilibrium.

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    File URL: http://arxiv.org/pdf/1402.6760
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    Paper provided by arXiv.org in its series Papers with number 1402.6760.

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    Date of creation: Feb 2014
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    Handle: RePEc:arx:papers:1402.6760

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    1. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    2. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, Springer, vol. 13(1), pages 121-150, January.
    3. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 18(3), pages 385-426.
    4. Ainslie, George, 1991. "Derivation of "Rational" Economic Behavior from Hyperbolic Discount Curves," American Economic Review, American Economic Association, American Economic Association, vol. 81(2), pages 334-40, May.
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