Faculty of Actuarial Science & Insurance Seminar with Fabio Viviano (Università della Calabria )

Abstract

This work proposes a continuous-time joint mortality model for actuarial valuations and risk analyses of life insurance liabilities. The framework uses a common subordinator for the marginal survival processes, thus introducing a non-trivial dependence structure. We model the underlying processes using Linear Hypercubes, a new class of Itô processes whose properties have been widely discussed in the literature. As they belong to the class of polynomial processes, which extend the well-known and successful affine models, Linear Hypercubes display richer dynamics while maintaining analytical tractability. This feature enables us to derive closed-form solutions (up to the computation of a matrix exponential) for standard actuarial measures. In addition, a further peculiarity of the proposed mathematical framework is that it allows us to consider (without affecting its mathematical tractability) a stochastic evolution of interest rates and a possible dependence between mortality and financial risks. The combined joint-mortality and financial market model is then used to derive analytical pricing formulae relative to insurance contracts issued to multiple lives, such as joint-life insurance, joint-life and last-survivor annuities. We show how the proposed model provides a good fit to real data from a Canadian insurer and perform extensive numerical experiments.

Biography