Optimal investment with minimum performance constraints

We consider the portfolio problem of an investor whose wealth is constrained to be at least as large as that generated by investment in a stochastic benchmark portfolio. Using standard option pricing results, the optimal portfolio policy of a HARA-utility investor is derived explicitly. This policy is shown to be equivalent, at any point in time, to the investor's optimal unconstrained policy when he has contracted to paying out a proportion of the value of the benchmark portfolio at the terminal date. This proportion, which lies between zero and one, is smaller the more likely it is that the investor will strictly outperform the benchmark over the investment horizon. (C) 2001 Elsevier Science B.V. All rights reserved.