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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.

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File URL: http://www.econ.uconn.edu/working/2009-04.pdf
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Bibliographic Info

Paper provided by University of Connecticut, Department of Economics in its series Working papers with number 2009-04.

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Length: 38 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:uct:uconnp:2009-04

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Postal: University of Connecticut 341 Mansfield Road, Unit 1063 Storrs, CT 06269-1063
Phone: (860) 486-4889
Fax: (860) 486-4463
Web page: http://www.econ.uconn.edu/
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Related research

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

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References

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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. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  3. 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.
  4. Francis A. Longstaff & Sanjay Mithal & Eric Neis, 2004. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit-Default Swap Market," NBER Working Papers 10418, National Bureau of Economic Research, Inc.
  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. 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 1637-42, December.
  7. 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.
  8. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
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