# Premium valuation for a multiple state model containing manifold premium-paid states

## TL;DR

This paper develops a general matrix formula for calculating net period premiums in multi-state models, integrating actuarial techniques with graph optimization, applicable to complex dread disease insurance scenarios.

## Contribution

It introduces a novel combination of actuarial methods and graph optimization to derive a comprehensive formula for premiums in multi-state models.

## Key findings

- Derived a matrix formula for multi-state premiums
- Applied the model to lung cancer dread disease insurance data
- Demonstrated practical utility in real-world insurance analysis

## Abstract

The aim of this contribution is to derive a general matrix formula for the net period premium paid in more than one state. For this purpose we propose to combine actuarial technics with the graph optimization methodology. The obtained result is useful for example to more advanced models of dread disease insurances allowing period premiums paid by both healthy and ill person (e.g. not terminally yet). As an application, we provide analysis of dread disease insurances against the risk of lung cancer based on the actual data for the Lower Silesian Voivodship in Poland.