A Dynamic Value-at-Risk Portfolio Model

A mathematical dynamic portfolio allocation model with uncertainty is discussed. Introducing a value-at-risk under a condition, this paper formulates value-at-risks in a dynamic stochastic environment. By dynamic programming approach, an optimality condition of the optimal portfolio for dynamic value-at-risks is derived. It is shown that the optimal time-average value-at-risk is a solution of the optimality equation under a reasonable assumption, and an optimal trading strategy is obtained from the equation. A numerical example is given to illustrate our idea.

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