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Stochastic optimization applied to self-financing portfolio: does bequest matter?

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  • Saziye Gaziog-super-˜lu
  • Azize Bastıyalı-Hayfavi
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    Abstract

    The article studies stochastic optimization of an intertemporal consumption model to allocate financial assets between risky and risk-free assets. We use a stochastic optimization technique, in which utility is maximized subject to a self-financing portfolio constraint. The papers in literature have estimated the errors of Euler equations using data from financial markets. It has been shown that it is sufficient to test the first order Euler equation implied by the model. However, they all assume a constant consumption-wealth ratio that constrains the boundary conditions, hence influencing the coefficient of the risk premium. The main contribution of our article is that we drop the assumption of a constant consumption-wealth ratio. We have an analytical solution using a utility maximization model with a stochastic self-financing portfolio. We introduce a terminal condition of wealth with and without bequests. We also simulate the stochastic optimization with a self-financing portfolio, distinguishing risk neutral investors (γ-low) from high risk averse investors (γ-high). We show that the model with bequest has a higher level of wealth and a smoother decline of consumption over time than the model with no bequest at the end of the period. The model with no bequest has the same level of consumption and a sharp fall at the end of the period. Risk averse agents with high return assets have a higher amount of wealth than risk-neutral agents with lower return assets.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/00036840802112364
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Economics.

    Volume (Year): 42 (2010)
    Issue (Month): 30 ()
    Pages: 3831-3838

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    Handle: RePEc:taf:applec:v:42:y:2010:i:30:p:3831-3838

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    1. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    2. Kocherlakota, Narayana R, 1990. " Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result," Journal of Finance, American Finance Association, vol. 45(1), pages 175-90, March.
    3. Sydney C. Ludvigson & Martin Lettau, 2005. "Euler Equation Errors," 2005 Meeting Papers 487, Society for Economic Dynamics.
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    6. Selden, Larry, 1978. "A New Representation of Preferences over "Certain A Uncertain" Consumption Pairs: The "Ordinal Certainty Equivalent" Hypothesis," Econometrica, Econometric Society, vol. 46(5), pages 1045-60, September.
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    8. Christopher D. Carroll, 1996. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," NBER Working Papers 5788, National Bureau of Economic Research, Inc.
    9. Martin Lettau, 2000. "Cross-variable restrictions in Euler equations and risk premia," Applied Economics Letters, Taylor & Francis Journals, vol. 7(2), pages 99-101.
    10. John Y. Campbell & John H. Cochrane, 1994. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," CRSP working papers 412, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    11. Gurdip S. Bakshi & Zhiwu Chen, 1996. "The Spirit of Capitalism and Stock-Market Prices," CEMA Working Papers 511, China Economics and Management Academy, Central University of Finance and Economics.
    12. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
    13. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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