Linear Generalized Stochastic Systems for Insurance Portfolios

Abstract

We consider a typical portfolio of different insurance products and investigate the pricing process using the framework of a linear time invariant generalized stochastic discrete-time model. Moreover, we assume that, due to regulatory constraints, the resulting system is (regular) descriptor and calculate the solution using the tools of matrix pencil theory. Finally, we present a numerical application for two different portfolios.

Keywords:

• Descriptor systems
• Matrix pencil theory
• Non causality
• Pooling of insurance risks
• Singularities
• Solvency interaction

Mathematics Subject Classification:

• 62P05
• 91B30
• 91B66
• 93C55

The authors are very grateful to the reviewer and to the Associate Editor and Distinguished University Professor, Chris P. Tsokos, for their insightful comments and advices, which improved highly the quality of this article.