A benchmarking approach to optimal asset allocation for insurers and pension funds

We solve the optimal asset allocation problem for an insurer or pension fund by using a benchmarking approach. Under this approach the objective is an increasing function of the relative performance of the asset portfolio compared to a benchmark. The benchmark can be, for example, a function of an insurer's liability payments, or the (either contractual or target) payments of a pension fund. The benchmarking approach tolerates but progressively penalizes shortfalls, while at the same time progressively rewards outperformance. Working in a general, possibly non-Markovian setting, a solution to the optimization problem is presented, providing insights into the impact of benchmarking on the resulting optimal portfolio. We further illustrate the results with a detailed example involving an option based benchmark of particular interest to insurers and pension funds, and present closed form solutions.