Premium Pricing, Demand Function, and Equilibrium in Heterogenous Portfolio.

Abstract

A heterogenous portfolio is a collection of insureds, which can be grouped into several risk classes. The insurer determines premium pricing in each risk class, using a certain pricing function. Pricing function is a function that states the amount of the premium based on the number of insured in each class. Each class has its own demand function, which determines the number of insured in this class as a function of the premium. This thesis aims to study the interaction between the number of insured in each class of a heterogenous portfolio and its premium. First, the insurer determines the premiums based on some initial number of insured in each class. Then, market reacts by updating the number of the policyholders. As a consequence, the insurer updates the premium. This process repeats until a certain condition is satisfied. This process has been proved to have an equilibrium point. The characteristics of the equilibrium point are determined by the fixed-point theorem. Finally, to illustrate the theory, the calculation of premium based on a demand function in equilibrium point for five risk classes is applied using Mathematica software.