Financial Risk Measurement Of Insurance Companies Based On Catastrophe Theory

The business process of insurance company is affected by a variety of uncertain internal and external factors. The changes in these factors, especially unexpected changes, will lead to the financial risk changes in the property insurance company. There are two types of change in the insurance company’s financial risk, including gradual change and catastrophic change. This paper names the factors or events, which will lead to catastrophic change on financial risk of insurance company, as the financial mutation events, and aims at measuring the financial risk of insurance company by creating the catastrophe-theory-based risk measurement model, according to the jumping and discontinuous catastrophic change of the insurance companies’financial risk.Firstly, the paper describes the characteristics of the financial mutation events. Then the paper introduces the Poisson distribution to describe the distribution of the financial mutation events and the distribution of impact of the financial mutation events on the financial risk. Then the author figures out two expected values:the expected value of the time interval during which the property insurance company maintains a specific financial risk level, and the expected value of the financial mutation events’impact on the financial situation of insurance company during the specific time interval T. All these provide the ideas and basis for measuring the financial risk in considering the impact of the financial mutation events. On this basis, this paper introduces the catastrophe theory, describes its basic principle and mathematical model, and then analyzes the applicability of creating the property insurance companies’financial risk measurement model based on the catastrophe theory.This paper implements the extension method to identify and screen the property insurance company’s financial index and build the financial index system which needed by the financial risk measurement model. Based on the extension method, the author gets the financial indicators’degree membership, same as the value of correlation function, which is the basis for choosing the financial risk measurement model’s the control variables a, b. c, d. According to the size of the correlation value, the control variables can be ordered.On this basis, the author constructs the catastrophe-theory-based insurance company’s financial risk measurement model, in which the financial risk is state variable and the financial indicators are control variables, and data of all financial indicators are from "China Insurance Yearbook". Finally, this paper measures the financial risk of the22 sample property insurance companies in2009by using the catastrophe progression method, combining the insurance companies’different selected financial index systems based on the extension method.