A Large-Scale Optimization Model for Replicating Portfolios in the Life Insurance Industry

Replicating portfolios have recently emerged as an important tool in the life insurance industry, used for the valuation of companies' liabilities. This paper presents a replicating portfolio (RP) model for approximating life insurance liabilities as closely as possible. We minimize the L1 error between the discounted life insurance liability cash flows and the discounted RP cash flows over a multi-period time horizon for a broad range of different future economic scenarios. We apply two different linear reformulations of the L1 problem to solve large-scale RP optimization problems and also present several out-of-sample tests for assessing the quality of RPs. A numerical application of our RP model to empirical data sets demonstrates that the model delivers RPs that match the liabilities rather closely. The numerical analysis demonstrates that our model delivers RPs with excellent practical properties in a reasonable amount of time. We complete the paper with a description of an implementation of the RP model at a global insurance company.