Narrow Results

In this paper we study the pricing problem for a class of Universal Variable Life (UVL) insurance products, using the idea of “Principle of Equivalent Utility”. The main features of the UVL products include the varying (death) benefit based on both tradable and non-tradable investment incomes and “multiple decrement” cases. We formulate the pricing problem as stochastic control problems, and derive the corresponding HJB equations for the value functions. In the case of exponential utilities, we obtain the explicit pricing formulae in terms of the global, bounded solutions of a class of semilinear parabolic PDEs with exponential growth. The general insurance models with multiple decrements and random time benefit payments are discussed as well.

The paper surveys recent results on the finite element approximation of Hamilton-Jacobi-Bellman equations. Various methods are analyzed and error estimates in the maximum norm are derived. Also, a finite element monotone iterative scheme for the computation of the approximate solution is given and its geometrical convergence proved.