Premium Calculation Research Articles

PERHITUNGAN PREMI ASURANSI JIWA DWIGUNA PASUTRI SEBAGAI PENERAPAN PEMBELAJARAN MATEMATIKA EKONOMI

In learning mathematical economics, the calculation of life insurance premiums is a matter concerning the application of a combination of compound interest, probability, differential and integral. Life insurance with multilife concept is the one of ap- plied in actuarial mathematics. A functions, in the actuarial cal- culation, related to death sequence in multilife concept is called as contingent function. Usage that function in calculation of insurance premium will assist the insurer in giving the benet precisely.Contingent probabilities are resulted by multiplication be- tween the force of mortality of life in the last sequence of death which have been determined and probabilities of life all family member in multilife status. Insurance formulation is obtained by mutiplying this probabilities with vt discount factor and they are integrated by using the assumption of a uniform distribution of death throughout the year of age.

The credibility premiums based on estimated moment-generating function

ABSTRACTTraditionally, experience ratemaking is in principle based on the idea of Bühlmann’s credibility theory that, except for net premiums, was rarely applied to other premium calculation principles. This article uses Bühlmann’s credibility procedure to estimate moment-generating functions (MGFs) of risks and then deduces estimates of moments of those risks. For the premium calculation principles that can be expressed as functions of certain moments or more directly of the MGFs, this article develops a new type of experience ratemaking methods by means of the estimated MGFs and discusses their consistency and asymptotic normality. Numerical simulation shows that, under the Esscher and exponential premium principles, the new credibility estimates are better than existing credibilityestimates in the literature.

PENENTUAN MODEL PREMI TIDAK KONSTAN PADA ASURANSI DANA PENSIUN

Pension plan is an effort to anticipate the life of old on the day. In the pension program, there are two methods of normal due’s calculation to be paid by the insured each year, the Entry Age Normal method, namely calculation of normal dues with constant premiums and projected unit credit method, namely calculation of normal dues with Premium Increases Each year or is not constant. This paper wants to develop an inconstant premium calculation method with constant premium increase annually. Where the pension plan participants’ age when he joined the pension plan is 19 years and the retirement age on this contract is 55 years, with premium increases of 5% of the normal dues early. The large ratio of premiums is, for dues normal at the age of 19 years until the age of 28 years, but for dues normal at the age of 29 years to the age of 33 years and to normal dues at the age of 34 years old until the age of one year before retirement.

リスク学と確率論の狭間で

Although the mathematical bases of risk are not entirely derived from the probability theory, the two have a delicate and unique relationship. At the origin of the science of risk, insurance companies flourished in the 17th and 18th centuries, where the calculation of insurance premium was based on probabilistic concepts, especially those developed by Pascal. Distinguished mathematicians such as Huygens, Bernoulli, and Bayes all belonged to this era. The probability theory was often used for risk analysis with relatively simple structures such as chemicals and toxicology, and this tendency is still dominant today. However, as risk targets expanded to include complex and non-linear phenomena such as environmental and social risks, the conventional, simple probability theory proved inadequate. In particular, probabilistic tools cannot be used to assess the complex mechanisms of low-level radiation risk. Moreover, huge earthquakes and nuclear power plant meltdown incidents that have a low frequency of occurrence but devastating repercussions cannot be approached with the probability theory. The appropriate mathematical model for such risks has not yet been developed.

A nonparametric data mining approach for risk prediction in car insurance: a case study from the Montenegrin market

For prediction of risk in car insurance we used the nonparametric data mining techniques such as clustering, support vector regression (SVR) and kernel logistic regression (KLR). The goal of these techniques is to classify risk and predict claim size based on data, thus helping the insurer to assess the risk and calculate actual premiums. We proved that used data mining techniques can predict claim sizes and their occurrence, based on the case study data, with better accuracy than the standard methods. This represents the basis for calculation of net risk premium. Also, the article discusses advantages of data mining methods compared to standard methods for risk assessment in car insurance, as well as the specificities of the obtained results due to small insurance market, such as Montenegrin.

Dealing with drought in irrigated agriculture through insurance schemes: an application to an irrigation district in Southern Spain

Hydrological drought is expected to have an increasing impact on both crop and fruit yields in arid and semi-arid regions. Some existing crop insurance schemes provide coverage against water deficits in rain-fed agriculture. The Prevented Planting Program in the USA covers against drought for irrigated agriculture. However, drought insurance for irrigated agriculture is still a challenge for companies and institutions because of the complexity of the design and implementation of this type of insurance. Few studies have attempted to evaluate the risk of loss due to irrigation water scarcity using both stand-alone production functions and crop simulation models. This paper’s contributions are that it evaluates the suitability of AquaCrop for calculating drought insurance premiums for irrigated agriculture and that it discusses contract conditions and insurance design for hydrological drought risk coverage as part of a traditional insurance product, with on-field loss assessment in combination with a trigger index. This method was applied to an irrigation district in southern Spain. Our insurance premium calculation showed that it is feasible to apply this method provided that its data requirements are met, such as a large enough set of reliable small-scale yield and irrigation time series data, especially soil data, to calibrate AquaCrop. The choice of a trigger index should not be underestimated because it proved to have a decisive influence on insurance premiums and indemnities. Our discussion of the contract conditions shows that hydrological drought insurance must comply with a series of constraints in order to avoid moral hazard and basis risk.

Nonparametric estimation of risk measures of collective risks

Abstract We consider two nonparametric estimators for the risk measure of the sum of n i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order n. This framework matches the situation that nonlife insurance companies are faced with within the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by n can be seen as a suitable premium for each of the individual risks. For both estimators divided by n we derive a sort of Marcinkiewicz–Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate n is studied by means of Monte-Carlo simulations.

Empirical study on optimal reinsurance for crop insurance in China from an insurer's perspective

This study investigates the optimal reinsurance for crop insurance in China in an insurer's perspective using the data from Inner Mongolia, Jilin, and Liaoning, China. On the basis of the loss ratio distributions modeled by AnHua Crop Risk Evaluation System, we use the empirical model developed by Tan and Weng (2014) to study the optimal reinsurance design for crop insurance in China. We find that, when the primary insurer's loss function, the principle of the reinsurance premium calculation, and the risk measure are given, the level of risk tolerance of the primary insurer, the safety loading coefficient of the reinsurer, and the constraint on reinsurance premium budget affect the optimal reinsurance design. When a strict constraint on reinsurance premium budget is implemented, which often occurs in reality, the limited stop loss reinsurance is optimal, consistent with the common practice in reality. This study provides suggestions for decision making regarding the crop reinsurance in China. It also provides empirical evidence for the literature on optimal reinsurance from the insurance market of China. This evidence undoubtedly has an important practical significance for the development of China's crop insurance.

Моделирование суверенной премии за риск на развивающихся рынках капитала

Дмитрий Вячеславовчич Тимофеев - Национальный Исследовательский Университет "Высшая Школа Экономики". Электронная почта: DTimofeev@hse.ru
 Акции на развивающихся рынках капитала обычно стоят дешевле, чем аналоги с развитых рынков. Для учета этого обстоятельства в моделях дисконтированных денежных потоков (далее по тексту ДДП) практики традиционно используют специальную (ad-hoc) надбавку в ставке дисконтирования – суверенную (или страновую) премию. Предлагаемые в литературе варианты расчета данной премии не имеют надлежащего теоретического обоснования. Другой, менее распространенный метод учета рисков развивающейся страны, предполагает использование сценарного подхода. Однако и его трудно реализовать из-за проблемы калибровки параметров. Налицо проблема учета риска бизнеса развивающихся стран.Предлагается отказаться от идеи суверенной премии. Для оценки компании из развивающейся страны предлагается следующий порядок. 1) Рассчитывается теоретическая стоимость в модели ДДП, как если бы бизнес принадлежал к развитой стране. 2) Применяется дисконт, учитывающий риск развивающегося рынка. Дисконт получается в ходе анализа разниц мультипликаторов рынка акций страны по сравнению с развитыми аналогами. В результате этого проблема учета риска страны перестает быть «черной коробкой» (black box) и превращается в верифицируемую процедуру.В работе критически анализируется практика расчета ставок дисконтирования и связанная с ней теория. Дается теоретический анализ развивающихся стран с точки зрения новой институциональной экономики, осмысляющей природу страновых рисков. В настоящей работе показано, что важнейшим источником риска развивающейся страны являются неустойчивость права собственности, создающей асимметрию в ожидаемой стоимости бизнеса. Это связано с логикой действий власти стран естественного порядка, контролирующих ренту и не позволяющих возвышению невластных элит. Еще одно объяснение предполагает невозможность странам с экстрактивными политическими институтами преодолеть ловушку среднего дохода. Созидательное разрушение приводит к проигрышу элит-инкумбентов и нарождению новых экономических элит, заявляющих свои политические права. Чтобы подставить под контроль политический процесс, нарушаются права собственности, что определяет обсуждаемую в данной работе асимметрию стоимости. Другое следствие этого – остановка процесса развития и меньший ожидаемый рост от акции развивающейся страны по сравнению с аналогичной развитой

An Economic Analysis and Approach for Health Care Preparedness in a Substate Region.

To demonstrate the application of economics to health care preparedness by estimating the financial return on investment in a substate regional emergency response team and to develop a financial model aimed at sustaining community-level disaster readiness. Economic evaluation methods were applied to the experience of a regional Pennsylvania response capability. A cost-benefit analysis was performed by using information on funding of the response team and 17 real-world events the team responded to between 2008 and 2013. By use of the results of the cost-benefit analysis as well as information on the response team's catchment area, a risk-based insurance-like membership model was built. The cost-benefit analysis showed a positive return after 6 years of investment in the regional emergency response team. Financial modeling allowed for the calculation of premiums for 2 types of providers within the emergency response team's catchment area: hospitals and long-term care facilities. The analysis indicated that preparedness activities have a positive return on their investment in this substate region. By applying economic principles, communities can estimate their return on investment to make better business decisions in an effort to increase the sustainability of emergency preparedness programs at the regional level.

A SURVEY ON DISCRIMINATION DETERRENCE IN DATA MINING

For extracting useful knowledge which is hidden in large set of data, Data mining is a very important technology. There are some negative perceptions about data mining. This perception may contain unfairly treating people who belongs to some specific group. Classification rule mining technique has covered the way for making automatic decisions like loan granting/denial and insurance premium computation etc. These are automated data collection and data mining techniques. According to discrimination attributes if training data sets are biases then discriminatory decisions may ensue. Thus in data mining antidiscrimination techniques with discrimination discovery and prevention are included. It can be direct or indirect. . When choices are created depending on delicate features that period the discrimination is oblique. The elegance is oblique when choices are created depending on nonsensitive features which are strongly correlated with one-sided delicate ones. The suggested system tries to deal with elegance protection in information exploration. It suggests new improved techniques applicable for immediate or oblique elegance protection independently or both simultaneously. Conversations about how to clean coaching information sets and contracted information places in such a way that immediate and/or oblique discriminatory decision guidelines are transformed to genuine classification guidelines are done. New analytics to evaluate the utility of the suggested methods are suggests and comparison of these methods is also done.

English

For extracting useful knowledge which is hidden in large set of data, Data mining is a very important technology. There are some negative perceptions about data mining. This perception may contain unfairly treating people who belongs to some specific group. Classification rule mining technique has covered the way for making automatic decisions like loan granting/denial and insurance premium computation etc. These are automated data collection and data mining techniques. According to discrimination attributes if training data sets are biases then discriminatory decisions may ensue. Thus in data mining antidiscrimination techniques with discrimination discovery and prevention are included. It can be direct or indirect. When decisions are made based on sensitive attributes that time the discrimination is indirect. When decisions are made based on nonsensitive attributes which are strongly correlated with biased sensitive ones that time the discrimination is indirect. The proposed system tries to tackle discrimination prevention in data mining. It proposes new improved techniques applicable for direct or indirect discrimination prevention individually or both at the same time. Discussions about how to clean training data sets and outsourced data sets in such a way that direct and/or indirect discriminatory decision rules are converted to legitimate classification rules are done. New metrics to evaluate the utility of the proposed approaches are proposes and comparison of these approaches is also done.

Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework

Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in practice typically chosen as time-constant percentages on top of the best estimate transition intensities. We develop a risk-oriented method for the allocation of a total safety margin to the single safety margins at each point in time and each state. In a case study, we demonstrate the suitability of the proposed method in different frameworks. The results show that the traditional method yields an unwanted variability of the safety level with respect to time, whereas the variability can be significantly reduced by the new method. Furthermore, the case study supports the German 60 percent rule for the technical interest rate.

Zróżnicowanie składek na europejskim rynku ubezpieczeń komunikacyjnych OC

Compulsory insurance is an obligation, regulated by law to enter into an insurance contract. One such insurance is compulsory motor third party liability insurance of vehicle owners. Compulsory insurance often makes products offered by insurance companies standard. The aim of the study is to assess the standardization of offered motor third party liability insurance based on selected European Union countries, by analyzing the premiums and tariff variables and bonus-malus systems used in the process of calculation of the insurance premium.

Some Applications in Economy for Utility Functions Involving Risk Theory

We present in the first part of the article types of utility functions that can describe the behavior of the investor and their applications to optimize portfolio. The second part of the paper refers to applications in calculating insurance premiums aggregated risk in zero utility principle.

Telematics System in Usage Based Motor Insurance

For the premium calculation and billing process in the motor insurance, current billing models are very general and not optimally tailored for the end users. Important parameters such as mileage, driving behavior and types of roads driven are not considered for the premium calculation. Development of advanced information and communication systems, significant drop in the technology cost of ownership, as well as the necessity for market differentiation in the insurance industry, facilitated the appearance of new billing models in the motor insurance industry. The purpose of this paper is to demonstrate underlying principles of the technology facilitating new billing models in the motor insurance industry. This paper gives an overview of the system architecture of one of the telematics systems offered and used on the market, as well as the data model used in the billing process. The potential of such a system is demonstrated through the real case project implemented in Eastern Europe.

Statistics as a basis for discrimination in the insurance business

The European Court of Justice has held that as from 21 December 2012, insurers may no longer charge men and women differently on the basis of scientific evidence that is statistically linked to their sex, effectively prohibiting the use of sex as a factor in the calculation of premiums and benefits for the purposes of insurance and related financial services throughout the European Union. This ruling marks a sharp turn away from the traditional view that insurers should be allowed to apply just about any risk assessment criterion, so long as it is sustained by the findings of actuarial science. The naivete behind the assumption that insurers’ recourse to statistical data and probabilistic analysis, given their scientific nature, would suffice to keep them out of harm’s way was exposed. In this article, I look at the flaws of this assumption and question whether this judicial decision, whilst constituting a most welcome landmark in the pursuit of equality between men and women, has nonetheless gone too far by saying too little on the million dollar question of what separates admissible criteria of differentiation from inadmissible forms of discrimination.

ON SOME PROPERTIES OF A CLASS OF MULTIVARIATE ERLANG MIXTURES WITH INSURANCE APPLICATIONS

AbstractWe discuss some properties of a class of multivariate mixed Erlang distributions with different scale parameters and describes various distributional properties related to applications in insurance risk theory. Some representations involving scale mixtures, generalized Esscher transformations, higher-order equilibrium distributions, and residual lifetime distributions are derived. These results allows for the study of stop-loss moments, premium calculation, and the risk allocation problem. Finally, some results concerning minimum and maximum variables are derived and applied to pricing joint life and last survivor policies.

금융거래 고객정보 침해사고 보상보험의 구성 및 정책방향

개인정보는 금융거래의 성립조건이며 금융회사의 핵심자산이다. 그러나 정보사회의 부작용으로써 나타난 개인정보 침해사고는 중대한 사회적 위험이 되고 있으며, 이러한 위험은 개인과 회사의 실제적 피해로써 현실화되고 있다. 본 연구는 소비자의 손실 측면에서 개인정보 침해 사고로 인해 금융 분야에서 발생한 금전적, 정신적 손해 현황을 분석하고, 이러한 실제 손해를 최소화하기 위한 위험전가의 수단으로써 보험의 유용성을 제시하였다. 그리고 개인 정보 침해 사고 보상보험의 구성요소와 보험료의 산정원리를 검토하고 최종적으로 이러한 보험 제도를 활성화하기 위한 정책을 제안하였다. 위험관리의 한 방법으로써 보험은 소비자 보호와 회사의 재무적 건전성을 동시에 확보할 수 있는 유용한 수단이며, IT 리스크의 계량적 측정을 위한 기반을 제공할 수 있다. Personal information is a requisite for financial transactions as well as a core asset of financial companies. However, as a side effect of the information society, personal information infringements have emerged as significant social risks, causing realized loss to individuals and companies. This study analyzes results of financial and emotional loss in terms of consumer loss and also presents usefulness of insurance in order to minimize such actual damages as a means of risk transfer. In addition, this study investigates components and premium calculation principles of compensation insurance against personal information invasion and finally presents policies to activate these insurance product. As a method of risk management, insurance not only is a useful tool to guarantee consumer protection and companies' financial soundness simultaneously but also provides a basis of quantitative measurement of IT risks.

Characterization theorems for customer equivalent utility insurance premium calculation principle

Characterization theorems for several properties possessed by the customer equivalent utility insurance premium calculation principle are presented. Demonstrated theorems cover cases of additivity, consistency, iterativity, and scale invariance properties. Results are formulated in a form of necessary and sufficient conditions for attainment of the properties imposed on customer’s utility function. Obtained theorems are also valid for the customer zero utility premium calculation principle. We also demonstrate that for the customer zero utility principle subjected to pricing of only strictly positive risks, the class of the utility functions producing scale invariant premiums is larger than in the general case.