ALM models based on second order stochastic dominance

Abstract

We propose asset and liability management (ALM) models in which the risk of underfunding is modelled based on the concept of stochastic dominance. Investment decisions are taken such that the distribution of the funding ratio, that is, the ratio of asset to liabilities, is non-dominated with respect to second order stochastic dominance (SSD). In addition, the funding ratio distribution is close in an optimal sense to a user-specified target distribution. Interesting results are obtained when the target distribution is degenerate; in this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. As an application, we consider the financial planning problem of a defined benefit pension fund in Saudi Arabia.