# A review of the Markov model of life insurance with a view to surplus

## TL;DR

This paper systematically reviews Markov surplus models in life insurance, integrating probabilistic theory with practical UK experience, and extends the models to include dynamic cashflows like reversionary bonuses.

## Contribution

It introduces a systematic organization of Markov surplus models with multiple technical bases and expands the definition to include non-contractual cashflows, enhancing model applicability.

## Key findings

- Expanded the definition of 'technical basis' to include non-contractual cashflows.
- Developed systematic terms to incorporate dynamic, quasi-contractual cashflows.
- Applied models to practical examples like paid-up valuation and reversionary bonuses.

## Abstract

We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically based on one and two technical bases, including a suitable descriptive notation. Extending this to three technical bases to accommodate different valuation approaches leads us: (a) to expand the definition of 'technical basis' to include non-contractual cashflows recognized in the associated Thiele equation; and (b) to add new (mainly) systematic terms to the surplus. Making these cashflows dynamic or 'quasi-contractual' covers many real applications, and we give two as examples, the paid-up valuation principle and reversionary bonus on participating contracts.