COLLECTIVE RISK MODEL BASED ON COMPOUND POISSON-LINDLEY PROCESS WITH SARMANOV DEPENDENCE AND ITS APPLICATION FOR SPECTRAL RISK PREMIUM PRICING
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 an...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/72909 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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.
|
|---|