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Solving the Non-Linear Dynamic Asset Allocation Problem: Effects of Arbitrary Stochastic Processes and Unsystematic Risk on the Super Efficient Portfolio Space

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  • Kwamie Dunbar

    (University of Connecticut and Sacred Heart University)

Abstract

In this paper we propose a methodology that we believe improves the effectiveness of several common assumptions underlying Modern Portfolio Theory's dynamic optimization framework. The paper derives a general outline of a stochastic nonlinear-quadratic control for analyzing and solving a non-linear mean-variance optimization problem. The study first develops and then investigates the role of unsystematic (credit) risk in this continuous time stochastic asset allocation model where the wealth generating process has a non-negative constraint. The paper finds that given unsystematic risk, wealth constraints and higher order moments the market price of risk is non-constant and the investor's optimal terminal return may be lower than previously indicated by a number of classical models. This result provides a convenient solution to practitioners seeking to evaluate competing investment strategies.

Suggested Citation

  • Kwamie Dunbar, 2009. "Solving the Non-Linear Dynamic Asset Allocation Problem: Effects of Arbitrary Stochastic Processes and Unsystematic Risk on the Super Efficient Portfolio Space," Working papers 2009-04, University of Connecticut, Department of Economics.
    • Handle: RePEc:uct:uconnp:2009-04
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    References listed on IDEAS

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    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    2. Francis A. Longstaff & Sanjay Mithal & Eric Neis, 2005. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2213-2253, October.
    3. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    4. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    5. Kwamie Dunbar, 2009. "The Effects of Credit Risk on Dynamic Portfolio Management: A New Computational Approach," Working papers 2009-03, University of Connecticut, Department of Economics, revised Feb 2009.
    6. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    7. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    8. Stapleton, R C & Subrahmanyam, M G, 1983. "The Market Model and Capital Asset Pricing Theory: A Note," Journal of Finance, American Finance Association, vol. 38(5), pages 1637-1642, December.
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    More about this item

    Keywords

    Dynamic Optimization; Credit Risk; Mean-Variance Analysis; Linear Quadratic Control; Credit Default Swaps; Capital Market Line; Gram-Charlier expansion; unsystematic risks;

    JEL classification:

    • G0 - Financial Economics - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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