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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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    7. 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.
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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;
    All these keywords.

    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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