An operator splitting harmonic differential quadrature approach to solve Young’s model for life insurance risk

This paper is concerned with the numerical approximation of a mathematical model for life insurance risk that has been presented quite recently by Young (2007, 2008). In particular, such a model, which consists of a system of several non-linear partial differential equations, is solved using a new numerical method that combines an operator splitting procedure with the differential quadrature (DQ) finite difference scheme. This approach allows one to reduce the partial differential problems to systems of linear equations of very small dimension, so that pricing portfolios of many life insurances becomes a relatively easily task. Numerical experiments are presented showing that the method proposed is very accurate and fast. In addition, the limit behavior of portfolios of life insurances as the number of contracts tends to infinity is investigated. This analysis reveals that the prices of portfolios comprising more than five thousand policies can be accurately approximated by solving a linear partial differential equation derived in Young (2007, 2008).