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A large deviations approach to optimal long term investment

Author

Listed:
  • Huyên Pham

    (Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, UFR Mathématiques, Case 7012, Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France)

Abstract

We consider an investment model where the objective is to overperform a given benchmark or index. We study this portfolio management problem for a long term horizon. This asymptotic criterion leads to a large deviation probability control problem. Its dual problem is an ergodic risk sensitive control problem on the optimal logarithmic moment generating function that is explicitly derived. A careful study of its domain and its behavior at the boundary of the domain is required. We then use large deviations techniques for stating the value function of this criterion of outperformance management. This provides in turn an objective probabilistic interpretation of the usually subjective degree of risk aversion in CRRA utility function.

Suggested Citation

  • Huyên Pham, 2003. "A large deviations approach to optimal long term investment," Finance and Stochastics, Springer, vol. 7(2), pages 169-195.
    • Handle: RePEc:spr:finsto:v:7:y:2003:i:2:p:169-195
    Note: received: June 2001; final version received: May 2002
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Sid Browne, 1999. "Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark," Finance and Stochastics, Springer, vol. 3(3), pages 275-294.
    3. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. W. H. Fleming & S. J. Sheu, 2000. "Risk‐Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Large deviation; risk sensitive control; dynamic programming equation; optimal logarithmic moment generating function; benchmark; optimal portfolio;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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