Optimal Investment with Minimum Performance Constraints

The author considers the portfolio problem of an investor whose wealth is constrained to be at least as large as that generated by investment in a benchmark portfolio. Using standard option pricing results, the optimal portfolio policy of a HARA-utility investor is derived explicitly and is shown to be equivalent, at any point in time, to this investor's optimal unconstrained policy when he has contracted to paying out some proportion of the value of the benchmark portfolio at the terminal date. This proportion, which lies between zero and one, depends on the likelihood that the optimal policy will strictly outperform the benchmark over the horizon.