Modeling of an insurance system and its large deviations analysis

2010-12-01
We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R(2). The claim sizes {X(i)} are an iid sequence with light tails. The interarrival times {tau(i)} between claims are also iid and exponentially distributed. There is a fixed premium rate cl that the customers pay; c < c(1) of this rate goes to the reinsurance company. If a claim size is greater than R the reinsurance company pays for the claim. We study the bankruptcy of this system before it is able to handle N number of claims. It is assumed that each company has initial reserves that grow linearly in N and that the reinsurance company has a larger reserve than the insurance company. If c and c(1) are chosen appropriately, the probability of bankruptcy decays exponentially in N. We use large deviations (LD) analysis to compute the exponential decay rate and approximate the bankruptcy probability. We find that the LD analysis of the system decouples: the LD decay rate gamma of the system is the minimum of the LD decay rates of the companies when they are considered independently and separately. An analytical and numerical study of gamma as a function of (c. R) is carried out.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Suggestions

Valuation of life insurance contracts using stochastic mortality rate and risk process modeling
Çetinkaya, Şirzat; Hayfavi, Azize; Department of Financial Mathematics (2007)
In life insurance contracts, actuaries generally value premiums using deterministic mortality rates and interest rates. They have ignored them stochastically in most of the studies. However it is known that neither interest rates nor mortality rates are constant. It is also known that companies may encounter insolvency problems such as ruin, so the ruin probability need to be added to the valuation of the life insurance contracts process. Insurance companies should model their surplus processes to price som...
Discrete-time surplus process for takaful insurance with multiple threshold levels
Achlak, Arham; Kestel, Sevtap Ayşe; Tank, Fatih; Department of Actuarial Sciences (2016)
Takaful is a type of insurance system whose participants contribute a certain sum of money to a common pool in order to guarantee each other against predefined losses. Over the past few years, the global Takaful industry has maintained solid growth trajectory with significant untapped potential across several markets. For this reason, there have been numerous researches conducted on the efficiency of Takaful system, but only few of them approach its actuarial aspect. This study aims to construct a new risk ...
Utilization of outlier-adjusted lee-carter model in mortality estimation on whole life annuities
Yavrum, Cem; Selçuk Kestel, A. Sevtap.; Department of Actuarial Sciences (2019)
Annuity and its pricing are very critical to the insurance companies for their financial liabilities. Companies aim to adjust the prices of annuity by choosing the forecasting model that fits best to their historical data. While doing it, there may be outliers in the historical data influencing the model. These outliers can be arisen from environmental conditions and extraordinary events such as weak health system, outbreak of war, occurrence of a contagious disease. These conditions and events impact morta...
The Comparison of risk measures on claim distributions: Turkish motor insurance case
Telkes, Cansu; Kestel, Sevtap Ayşe; Tank, Fatih; Department of Actuarial Sciences (2018)
In this thesis, the impact of various risk measures on pricing methodology of automobile insurance product by using the historical claim data which is obtained from one of the most reputable insurance company in Turkey is investigated. To model the distribution of claim experience for pricing methodology, four right skewed distributions are chosen, namely Gamma, Weibull, Lognormal and Pareto. Two classical methods, which are methods of moment estimation and maximum likelihood estimation, are used to estimat...
Optimal premium allocation under stop-loss insurance using exposure curves
Mert, Özenç Murat; Kestel, Sevtap Ayşe (2021-11-01)
Determining the retention level in the stop-loss insurance risk premium for both insurer and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts. The dependence between the costs of insurer and reinsurer is expressed as a function of retention (d) and maximum-cap (m) levels. Based on the maximum degree of correlation, the optimal levels for d and m are derived under certain claim...
Citation Formats
A. D. Sezer, “Modeling of an insurance system and its large deviations analysis,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 535–546, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/29926.