Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
Subadditivity and Parameter Uncertainty of VaR and Solvency Capital Requirement (SCR) in Tail Region of a Non-life Insurance Portfolio
1
42
EN
Jan
Dhaene
Professor, KU Leuven
jan.dhaene@kuleuven.be
Ahmad
Salahnejhad Ghalehjooghi
PhD Candidate of Actuarial Science, Maastricht University
salahnejhad@maastrichtuniversity.nl
<em>Although VaR is important due to its widespread usage to obtain overall Solvency Capital Requirement (SCR) in the standard model of Solvency II directives, it is not subadditive. Without subadditivity, the summation of SCRs of different lines of business, which is usually used by risk managers, may underestimate overall SCR for an insurance company. This research examines the subadditivity property of VaR for fat-tailed insurance losses in a dependent structure. The foundation of the paper is based on Danielson et al (2013), a study on subadditivity of VaR in the tail region of asset return data. We applied the same idea by using Generalized Pareto Distribution (GPD) to model the fat-tailed insurance losses and capture their dependence structure by the Gumbel-Houggard copula through the tail of the joint distribution. Using these instruments, we proposed a simulation method to examine subadditivity of VaR and SCR. By empirical methods, we found that, similar to the fat-tailed asset returns, insurance losses are also more subadditive in tail region. We found that only going deep into the tail, will not guarantee monotonically more subadditivity, where “Variation of dependence” and “shape parameter” through the tail of the distribution are other important factors that Danielson et al didn’t take into account. More specially, when the correlation measure in different thresholds is changed, subadditivity of VaR deviates to increase monotonically in the tail. Furthermore, we observed that the uncertainty of VaR estimation is not always monotonically increasing through the tail; it may increase in the first thresholds of the right tail, it decreases in higher thresholds.</em>
Copula,Excess of loss Contract,Solvency Capital Requirement (SCR),Stop-loss Contract,Subadditivity,Tail Dependence,VAR
http://ijri.irc.ac.ir/article_43265.html
http://ijri.irc.ac.ir/article_43265_1aa7524a55d4de28aa3b59578af5eacd.pdf
Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
Ordering Properties of the Smallest Claim Amount from Two Heterogeneous Generalized Exponential Portfolios and their Application to Insurance
43
63
EN
Ghobad
Barmalzan
PhD Candidate of Statistics, Shahid Beheshti University
ghobad.barmalzan@gmail.com
Amir.T.
Payandeh Najafabadi
Associate Professor, Shahid Beheshti University
<strong>Abstract</strong><br /> <em>Suppose </em> <em> is a set of non-negative random variables with </em> <em> having the distribution function generalized exponential, for </em> <em>, and </em> <em> are independent Bernoulli random variables, independent of the </em> <em>'s, with </em> <em>, </em> <em> . Let </em> <em> , for </em> <em> It is of interest to note that in actuarial science, it corresponds to the claim amount in a portfolio of risks.</em> <em>In this paper, it’s been tried to discuss the stochastic comparison between the smallest claim amounts in the sense of the usual stochastic order using the concept of vector weakly submajorization and under certain conditions. We obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters </em><em>changes to another matrix in a mathematical sense and finds an upper bound for the survival function of smallest claim amount. The results established here extend some well-known results in the literature and show that larger stochastic order smallest claim amount lead to the desirable property of uniformly larger Value-at-Risk.</em>
Smallest Claim Amounts,Value-at-Risk,Generalized Exponential Distribution,Weakly Sunmajorization,Matrix Majorization,Schur-Convexity,Schur-Concavity
http://ijri.irc.ac.ir/article_43266.html
http://ijri.irc.ac.ir/article_43266_b1c5ac5b3809027904b638457170f156.pdf
Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
The Effect of Risk Aversion on Lapsation in Iran Life Insurance Market
65
83
EN
Ghadir
Mahdavi
Associate Professor, Allameh Tabataba'i University
mahdavi@irc.ac.ir
Mojtaba
Abed
MS in Actuarial science, Allameh Tabataba'i University
m85_abed@yahoo.com
<br /> <em>Adverse selection is a real obstacle in the life insurance industry describing a situation in which information asymmetry leads riskier policyholders to purchase more insurance coverage. Such kind of adverse selection is static adverse selection in the time of purchasing policy. Asymmetric information results in another type of adverse selection called dynamic adverse selection. Dynamic adverse selection occurs when </em><em>individuals with high level of risk aversion (low-risk individuals) </em><em>lapse a policy during the period of contract. Inversely, dynamic advantageous selection occurs when </em><em>individuals with low level of risk aversion (high-risk individuals) </em><em>lapse their contracts when policy is effective.</em><br /> <em>In this article, we investigate the effects of Risk Aversion on the lapsation of life insurance policies in Iranian Life Insurance Market. A Binary logistic analysis is used to examine the effects of risk aversion on lapsation of life insurance policies. </em><br /> <em>Results show that the lapsation of life insurance policies has a negative correlation with the risk aversion level of policyholders. Age, gender and marital status as risk aversion proxies affect significantly the lapsation of life insurance policies. </em><em>Since individuals with low level of risk aversion (high-risk individuals) lapse their contracts more than individuals with high level of risk aversion (low-risk individuals), dynamic Advantageous Selection is evident in Iranian life Insurance</em><em> Market</em><em>. </em>
Dynamic Advantageous Selection,Dynamic Adverse Selection,Lapsation,and Risk Aversion
http://ijri.irc.ac.ir/article_43267.html
http://ijri.irc.ac.ir/article_43267_3e8361b127ee4acb4d51824717d4960c.pdf
Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
Pricing Unemployment Insurance in Iran
85
109
EN
Reza
Ofoghi
Assistant Professor, Allameh Tabataba'i University
r.ofoghi@yahoo.com
Ramyar
Ebne Abbas
MSc in Actuarial Science, Allameh Tabataba'i University
r.ebneabbas@gmail.com
<em>Employees are always concerned about losing their jobs, or in other words, losing their income resources. For this purpose, governments require strong protection system to cover these concerns. The Unemployment Insurance (UI) program can be used to achieve this goal. </em><br /> <em>Based on article five of Iranian unemployment Insurance law, premium is 4% of employee’s salary while employer and government contributions are 3% and 1%, respectively. So, there are great concerns about the financial pressure on the government regarding implementation of this law. </em><br /> <em>In this paper, we price UI based on the insurance history of employee and the duration of unemployment. We use the Weibull distribution for finding duration of unemployment, and finally equivalence principle is applied to find the fair UI premium rate. Our findings indicate that the UI rate is less than 4% which is lower than current UI rate in Iran set by law. Consequently, government contribution can be eliminated, which will result in reduction of government concerns over the required budget.</em>
Unemployment Insurance,Equivalence Principle,CAPM,Weibull distribution,Iran’s UI scheme,Job search theory
http://ijri.irc.ac.ir/article_43269.html
http://ijri.irc.ac.ir/article_43269_fe56ade379671f0b70c73cb9e592795a.pdf
Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
The Relationship between Life Insurance Demand and Economic Growth in Iran
111
131
EN
Atousa
Goudarzi
Assistant Professor, Allame Tabataba'i University
atousagoodarzi@yahoo.com
Shima
Sakhaei
MA of Actuarial Science, Allame Tabataba'i University
sakhaei.sh@gmail.com
<em>A well-developed insurance sector, as a financial market is necessary for the economic growth since it provides long-term funds for physical and social infrastructures and strengthens risk-taking abilities. This study aims to examine the existence of a relationship between the growth of life insurance demand and the economic growth in Iran. </em><br /> <em>Using econometric methodology, the data for the period of 1348-1389 were collected from the Iranian national data center, then by estimating the Vector Autoregressive (VAR) model</em> <em>along with several time series tests such as unit root test, co-integration test, granger causality test, impulse response function & variance decomposition of forecast errors, the econometric results indicate that life insurance sector growth contributes positively to economic growth.</em><br /> <em> </em>
life insurance sector growth,Economic Growth,Vector Autoregressive (VAR) model,time series
http://ijri.irc.ac.ir/article_43270.html
http://ijri.irc.ac.ir/article_43270_d652657c3b6e0d009c47ee61112b1380.pdf
Insurance Research Center
Iranian Journal of Risk and Insurance
1
1
2015
05
01
A Statistical Approach to Money Laundering Detection in Insurance Company Using Genetic Algorithm
133
147
EN
Mir Mahdi
Seyed Esfahani
Associated Professor, Amirkabir University of Technology
msesfahani@aut.ac.ir
Somayeh
Molaei
PhD Candidate of Industrial Engineering, Iran University of Science and Technology.
molaei@aut.ac.ir
Akbar
Esfahanipour
Assistant Professor, Amirkabir University of Technology
esfahaa@aut.ac.ir
<em>Insurance companies are faced with the challenge of money laundering. Money laundering is a complex, dynamic and distributed process which exposes insurance companies to legal, operational and reputational risks. Previous studies in insurance investigate the fraud in insurance and proposed different methods for fraud detection, while money laundering as a crucial phenomenon in insurance, which exposes the insurance company to risk, is neglected. We explore the money laundering in insurance and propose an efficient statistical method to detect it.</em><br /> <em> In this paper we propose a useful strategy which aimed at stratified sampling instead of exhaustive inspection for detecting money laundering activities. This approach is based on a division of insureds into homogeneous subgroups (strata). For this purpose, we firstly formulate the stratification task as a non-linear restricted optimization problem, in which the variance of overall amount of money laundered due to money laundering activities is minimized. Then we develop the metaheuristic approach namely the genetic algorithm (GA) to compute the optimum number of subgroups. The results show that the near optimum number of strata is 600, which means that we should divide insureds into 600 groups and survey these samples instead of surveying all insureds.</em>
Money Laundering,Life Insurance,stratified sampling,Genetic algorithm,Design of experiments
http://ijri.irc.ac.ir/article_43271.html
http://ijri.irc.ac.ir/article_43271_59da81c79396970cbb3bfd3dfaeb2d68.pdf