Lognormal and log-logistic distribution mixture analysis and application

In this paper, we analyze a mixture of Lognormal and Log-Logistic distribution. We estimate the parameters of the introduced distribution by using the expectation-maximization (EM) algorithm. Various phenomena in the field of medicine and economy could be modeled by this mixture. In this paper, it is used to construct new mortality model for determining the unisex premium rates in life insurance. The application of the model is illustrated in the case of Serbian population and its advantages are presented in the context of life insurance premium calculation.

Decomposition of Natural Catastrophe Risks: Insurability Using Parametric CAT Bonds

Nat Cat risks are not insurable by traditional insurance mainly because of producing highly correlated losses. The source of such correlation among buildings of a region subject to a natural hazard is discussed. A decomposition method is proposed to split Nat Cat risk into idiosyncratic (and hence insurable) risk and systematic risk (carrying the correlated part). It is explained that the systematic risk can be transferred to capital markets using a set of parametric CAT bonds. Premium calculation is presented for insuring the decomposed risk. Portfolio risk-return trade-off measures for investing on the parametric CAT bond are derived. Multi-regional and multi-hazard parametric CAT bonds are introduced to reduce the risk of the investment. The methodology is applied on a region with about 3000 residential buildings subject to flood hazards.

PERHITUNGAN PREMI MURNI PADA SISTEM BONUS MALUS UNTUK FREKUENSI KLAIM BERDISTRIBUSI BINOMIAL NEGATIF DAN BESAR KLAIM BERDISTRIBUSI WEIBULL PADA DATA ASURANSI KENDARAAN BERMOTOR DI INDONESIA

System bonus malus is one of the systems offered by an insurance company where the risk premium calculation is based on the claim history of each policyholder. In study will be discussed premium calculation in system, bonus malus where the frequency of claims has a negative binomial distribution and the size of claims is Weibull distribution on motor vehicle insurance data in Indonesia. This method will producesystem an bonus malus optimal by finding the posterior distribution using Bayes analysis. As the application material used secondary data from the recording results obtained from the general insurance company PT. XYZ in 2014, data contains data on the frequency of claims and the amount ofclaims partial loss of policyholders forinsurance products for comprehensivemotor vehicle insurance category 8 regions 3.The results of the implementation show that the premiums with the system are bonus malus optimalconsidered fair enough because the premiums paid by policyholders insurance that extends the policy in the following year is proportional to the risk it faces, where the premium to be paid by each policyholder is based on past claims history. Keywords: system bonus malus, negative binomial distribution, Weibull distribution, comprehensive, partial loss.

An Actuarial Approach for Modeling Pandemic Risk

In this article, a model for pandemic risk and two stochastic extensions is proposed. It is designed for actuarial valuation of insurance plans providing healthcare and death benefits. The core of our approach relies on a deterministic model that is an efficient alternative to the susceptible-infected-recovered (SIR) method. This model explains the evolution of the first waves of COVID-19 in Belgium, Germany, Italy and Spain. Furthermore, it is analytically tractable for fair pure premium calculation. In a first extension, we replace the time by a gamma stochastic clock. This approach randomizes the timing of the epidemic peak. A second extension consists of adding a Brownian noise and a jump process to explain the erratic evolution of the population of confirmed cases. The jump component allows for local resurgences of the epidemic.

PENERAPAN HUKUM MORTALITA MAKEHAM UNTUK PENENTUAN NILAI CADANGAN PREMI ASURANSI JOINT LIFE DENGAN METODE FACKLER

Joint life insurance is life insurance with an amount of more than one person, where the benefits are paid when one of the insured dies. The possibility of insurance companies will suffer losses if the claims that occur are more than predicted, so the premium reserve calculation is required. In this study, reserves were calculated using the Fackler method based on the Indonesian Mortality Table 2011 and the Makeham Assumption Mortality Table. The Indonesian Mortality Table 2011 was analyzed for the estimated parameters contained in the Makeham Assumption Mortality Table. Then the premium calculation and premium reserve calculation are done using the Fackler method based on the Makeham Assumption Mortality Table and the comparison uses the Indonesian Mortality Table 2011. The results of the calculation of the premiums based on the Makeham Assumption Mortality Table are greater than using the Indonesia Mortality Table 2011, while the premium reserve results are greater using the Indonesian Mortality Table 2011 than using the Makeham Assumption Mortality Table. This is because the chances of survival based on the Makeham Assumption Mortality Table are smaller than the Indonesian Mortality Table 2011.