COLLECTIVE RISK MODEL BASED ON COMPOUND POISSON-LINDLEY PROCESS WITH SARMANOV DEPENDENCE AND ITS APPLICATION FOR SPECTRAL RISK PREMIUM PRICING

• Main Author: Ryan Tjahjono, Venansius
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/72909
• Institution: Institut Teknologi Bandung

An insurance scheme is an activity to transfer risk from policyholders to insurers. A statistical model is required to inspect how much risk the insurance company will abide by, one of which is the collective risk model. The collective risk model is a random variable constructed from frequency and average severity random variables. The loss frequency random variable illustrates the number of incurred losses. While the average loss severity random variable provides information regarding how much loss has occurred. This study extends the loss frequency random variable into a stochastic process to make it more sensible. The Poisson-Lindley process is one of the stochastic process, which accommodates the overdispersion phenomena. Thus, the collective risk model is formed based on a compound Poisson-Lindley process. As for the average loss severity distribution, the gamma distribution and the Inverse Gaussian distribution are proposed. Both distributions are suitable for modeling data with positive skewness. In practice, it is often assumed that the frequency and the average severity are independent. However, recent studies have shown there is an interconnectedness between these two. To capture the dependence phenomenon between these two, a bivariate Sarmanov distribution is employed, hereinafter referred to as Sarmanov dependence. The Sarmanov dependence has the flexibility to combine two types of marginal probability functions. In the case of insurance, the type of probability function are discrete, for frequency, and continuous, for average severity. The results of collective risk modeling with a basis of the compound Poisson-Lindley process are then analyzed to obtain some statistical properties, such as expectation, variance, and correlation. Expected value and variance are used for pure premium and risk premium pricing, while the correlation measures the dependence of the frequency and the average severity. We also propose acquiring a spectral risk premium with an exponential risk aversion spectrum. The risk spectrum is used to adjust the risk premium, and the results are for insurance companies with a risk-averse type. In the empirical study, the Maximum Simulated Likelihood Estimation is used to estimate the collective risk model parameter based on the insurance loss data in India. The simulation results indicate that a compound Poisson-Lindley process with Inverse Gaussian distribution provides a higher log-likelihood value. As for the dependency phenomenon, with a correlation above 50%, it can potentially increase or decrease the premium. Herefore, if the assumption of independence is used, the premium results may be underrated or overrated. In addition, the spectral risk premium provides a premium value that is more costly when compared to the risk premium. This fact suggests that the spectral risk premium suits insurance companies with a risk-averse type.