Abstract

We consider the insurance company as a physical system which is immersed in its en- vironment (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 Esscher principle, the well-known formula in actuary for premium calculation. We simulate the case of car insurance for quantitative comparison.