Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space

TL;DR

This paper introduces a novel model for insurance states using Markov jump processes with non-countable state spaces, leading to a new form of Thiele's differential equation for reserve calculation in disability insurance.

Contribution

It extends traditional Markov models by incorporating more general state spaces and derives a new Thiele's differential equation for improved reserve calculations.

Findings

Derived a new Thiele's differential equation for complex state spaces

Enabled consistent reserve calculations in disability insurance

Applied model to rehabilitation rate scenarios

Abstract

In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability insurance, we propose in this paper a model for insurance states based on Markov jump processes with more general state spaces. We use this model to derive a new type of Thiele's differential equation which e.g. allows for a consistent calculation of reserves in disability insurance based on two-parameter continuous time rehabilitation rates.