Nonlinear reserving and multiple contract modifications in life insurance

TL;DR

This paper extends the stochastic Thiele equation and Cantelli Theorem to non-Markovian models, providing a recursive scheme for calculating multiple contract modifications in life insurance with reserve-dependent cash flows.

Contribution

It introduces a novel extension of key actuarial tools to non-Markovian frameworks and develops a recursive method for multiple contract modifications.

Findings

Extended Thiele equation to non-Markovian models

Generalized Cantelli Theorem for complex modifications

Recursive scheme for multiple contract modifications

Abstract

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.