Non-Life Insurance Pricing : Statistical Mechanics Viewpoint

TL;DR

This paper models non-life insurance pricing using statistical mechanics, deriving premiums via canonical ensemble theory and comparing with traditional actuarial methods through simulations.

Contribution

It introduces a novel approach to insurance pricing by applying statistical mechanics, specifically the canonical ensemble, and compares it with established actuarial formulas.

Findings

Premiums derived from statistical mechanics match traditional methods in simulations.

The approach provides a new perspective on insurance market interactions.

Simulation results validate the theoretical model.

Abstract

We consider the insurance company as a physical system which is immersed in its environment (the financial market). The insurer company interacts with the market by exchanging the money through the payments for loss claims and receiving the premium. Here in the equilibrium state we obtain the premium by using the canonical ensemble theory, and compare it with the {\it Esscher} principle, the actuaristic well known formula for premium calculation. We simulate the case of automobile insurance for quantitative comparison.