OPTIMAL INVESTMENT OF A LIFE INTEREST

We consider the problem of a trustee faced with investing a sum of money, the interest from which will be received by one party (the life-tenant) during his lifetime while the capital will go to another party (the survivor) on the death of the life-tenant. We assume mat there are n + 1 assets in which the trustee may invest— n risky assets of geometric Brownian motion type and one nonrisky asset. Under assumptions as to the utility functions of the two parties, we find the collection of Pareto optimal investment strategies for the trustee together with the corresponding payoffs. We do this by optimizing the payoff of the Lagrangian for the problem. We go on to present the Nash optimal solution for the trustee.