Generation of Option-Like Investment Profiles in Open-Ended Funds

Abstract

Most of the financial litterature on optimal investment assumes that there exists both an initial and a final date between which the investment policy has to made optimal.. In practice, however, fund managers does not really have a starting point nor a final point at which the efficiency of their strategy can be assessed. The aim of this paper to explore the optimisation program of an open ended fund manager. Our contribution is twofold.

First we introduce an endogenous reference level process which replaces the traditional "initial value". This allows us to derive new state variables. Those state variables, which can be interpreted as averaged past returns, are well suited to formulate open-ended investment issues.

Second, combining the above with a random investment time, we formulate and solve the problem of how a wealth process can be made as close as possible to an option profile in an open-ended framework. In the risk-neutral limit, the result is obtained as the solution of an ODE. Some simulations illustrate the practical effectiveness of our approach.