Trust Fund Management in a Black-Scholes World, with Implications for Collective Pension Funds

Abstract

In intertemporal choice, there are situations in which the primary purpose of a social planner is to maintain a steady level of consumption by future generations, rather than to realize an increasing consumption path. For instance, this may hold for governors of an endowment fund. Preference for stability can be expressed by employing a utility function that has a saturation level. In the present paper, the consequences are investigated of adopting a saturated utility function within a stochastic economic environment. Policies are derived both for a utilitarian planner, who works on the basis of an aggregated social welfare function, and for a Rawlsian planner who equalizes the benefits experienced by all recipients. The Rawlsian neutrality principle appears natural for social planners aiming to provide steady income. However, various interpretations of the principle are possible in the stochastic case, which can lead to substantially different policies. Moreover, under saturated utility, the Rawlsian policies do not satisfy time consistency in the most commonly used sense.