A stochastic-programming approach to integrated asset and liability management of insurance products with guarantees

Abstract

In recent years insurance products have become more complex by providing investors with various guarantees and bonus options. This increase in complexity has provided an impetus for the investigation into integrated asset- and liability-management frameworks that could realistically address dynamic portfolio allocation in a risk-controlled way. In this paper the authors propose a multi-stage dynamic stochastic-programming model for the integrated asset and liability management of insurance products with guarantees that minimises the down-side risk of these products. They investigate with-profit guarantee funds by including regular bonus payments while keeping the optimisation problem linear. The uncertainty is represented in terms of arbitragefree scenario trees using a four-factor yield-curve model that includes macroeconomic factors (inflation, capacity utilisation and the repo rate). They construct scenario trees with path-dependent intermediate discrete yield-curve outcomes suitable for the pricing of fixed-income securities. The main focus of the paper is the formulation and implementation of a multi-stage stochasticprogramming model. The model is back-tested on real market data over a period of five years.

KEYWORDS Minimum guarantees; asset and liability management; stochastic programming; portfolio optimisation