Premium Forecasting of an Insurance Company: Automobile Insurance

TL;DR

This paper models the financial performance of an automobile insurance company to determine optimal premiums, analyze profitability thresholds, and assess risk and ruin probabilities based on insurance parameters.

Contribution

It introduces a statistical framework for predicting insurance company profitability and identifies the optimal premium to maximize profit while analyzing risk factors.

Findings

Existence of a crossover premium p_c below which the company incurs losses.

Derivation of the optimal premium p_{opt} that maximizes profit.

Quantitative analysis of ruin probability and financial risk at different premium levels.

Abstract

We present an analytical study of an insurance company. We model the company's performance on a statistical basis and evaluate the predicted annual income of the company in terms of insurance parameters namely the premium, total number of the insured, average loss claims etc. We restrict ourselves to a single insurance class the so-called automobile insurance. We show the existence a crossover premium p_c below which the company is loss-making. Above p_c, we also give detailed statistical analysis of the company's financial status and obtain the predicted profit along with the corresponding risk as well as ruin probability in terms of premium. Furthermore we obtain the optimal premium p_{opt} which maximizes the company's profit.