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Maximin setting for investment problems and fixed income management with observable but non-predictable parameters

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  • Nikolai Dokuchaev

Abstract

We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be larger than the number of driving Brownian motions. We assume that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are not necessary adapted to the driving Brownian motion, and their distributions are unknown, but they are supposed to be currently observable. Admissible strategies are based on current observations of the stock prices and the aforementioned parameters. The optimal investment problem is stated as a problem with a maximin performance criterion. This criterion is to ensure that a strategy is found such that the minimum of utility over all distributions of parameters is maximal. Then the maximin problem is solved for a very general case via solution of a linear parabolic equation.

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  • Nikolai Dokuchaev, 2002. "Maximin setting for investment problems and fixed income management with observable but non-predictable parameters," Papers math/0207259, arXiv.org.
    • Handle: RePEc:arx:papers:math/0207259
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    References listed on IDEAS

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    1. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    2. N. Dokuchaev & U. Haussmann, 2001. "Optimal portfolio selection and compression in an incomplete market," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 336-345, March.
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