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The relaxed investor and parameter uncertainty

Author

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  • L.C.G. Rogers

    (University of Bath, Department of Mathematical Sciences, Bath BA2 7AY, UK Manuscript)

Abstract

We firstly consider an investor faced with the classical Merton problem of optimal investment in a log-Brownian asset and a fixed-interest bond, but constrained only to change portfolio (and, if relevant, consumption) choices at times which are a multiple of h. We show that the cost of this constraint can be well described by a power series expansion in h, the first few terms of which we determine explicitly. Typically, this cost is not too large. We then compare this with the cost of parameter uncertainty, as modelled by supposing that the rate of return on the share has a prior Gaussian distribution. We find that the effect of parameter uncertainty is typically bigger than the effects of infrequent policy review.

Suggested Citation

  • L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    • Handle: RePEc:spr:finsto:v:5:y:2001:i:2:p:131-154
    Note: received: November 1999; final version received: June 2000
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    More about this item

    Keywords

    Merton consumption problem; Merton investment problem; time lag; parameter uncertainty;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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