Premium Calculation Research Articles

Coffee export insurance premium estimates from Sumatera Utara Province in international market

Calculation of insurance premiums can be analysed based on a area’s yield index, weather and price volatility. This study reviewed based on the movement of Sumatera Utara coffee export prices. The purpose is to calculate and review the premium insurance for Sumatera Utara coffee exports in the international market. The research location was determined purposively with snowball sampling technique. The research data consisted of primary data which was collected by questionnaire and secondary data from Association of Indonesian Coffee Exporters Regional of Sumatera Utara and province’s statistical data. The coverage amount 32,458,011.5 IDR, it is obtained from calculation of costs incurred by exporters. The Black-Scholes method is used to determine the value of coffee export insurance premiums based on the export prices. The analysis shows that the higher trigger also increases the insurance premium, because the higher risk, so the higher premium.

ANALISIS CADANGAN MANFAAT DENGAN MENGGUNAKAN METODE RETROSPEKTIF PADA ASURANSI JIWA BERJANGKA

Perusahaan asuransi merupakan salah satu perusahaan yang melindungi nasabahnya dari suatu kejadian yang tidak diinginkan di masa yang akan datang. Perusahaan asuransi jiwa harus menyiapkan dana cadangan manfaat untuk diberikan kepada nasabah, jika nasabah mengalami risiko kematian di masa yang akan datang. Oleh sebab itu, perusahaan asuransi harus mengelola dana cadangan manfaat agar perusahaan tidak mengalami kerugian. Tujuan dari penelitian ini adalah menghitung besar premi bersih tahunan dan menghitung besar cadangan manfaat pada asuransi jiwa berjangka. Metode yang digunakan untuk menghitung nilai cadangan manfaat adalah metode retrospektif. Hasil perhitungan premi bersih tahunan menyatakan bahwa besar premi bersih tahunan untuk nasabah yang berusia lanjut lebih besar daripada nasabah yang berusia lebih muda untuk jangka waktu yang sama. Sedangkan nilai cadangan manfaat asuransi akan terus meningkat pada awal kontrak asuransi dimulai dan nilai cadangan asuransi akan terus menurun menuju nol pada akhir kontrak asuransi. Hal ini dikarenakan pada awal kontrak asuransi pendapatan perusahaan yang diperoleh dari pembayaran premi bersih tahunan akan lebih besar daripada jumlah manfaat yang harus dibayarkan.

Premium Calculation for Insurance Businesses Based on Cyber Risks in IP-Based Power Substations

Insurance is a promising risk transfer tool against switching cyberattacks on power grids that can disrupt operation and potentially lead to widespread outages. This paper emphasizes on a framework of premium calculation for cyber insurance businesses by modeling potential electronic intrusion with steady-state simulation results and its direct hypothesized impacts. The proposed actuarial framework models the operational monetary losses with the hypothesized power outages based on the cyber-reliability assessment and its expected mean time to restore power (MTTRP). The ruin probability is employed as the fundamental formula to determine the feasible insurance premium pool. Hypothesized spatial correlation studies on multiple substation contingencies associated with switching attacks have shown estimated operational losses and expected duration of power restoration, which is translated into the calculation of insurance premium. The proposed actuarial framework is validated using generalized IEEE test cases with modified parameters on substations. The potential implications of grid's hypothetical scenarios are discussed.

A Bivariate Compound Dynamic Contagion Process for Cyber Insurance

As corporates and governments become more digital, they become vulnerable to various forms of cyber attack. Cyber insurance products have been used as risk management tools, yet their pricing does not reflect actual risk, including that of multiple, catastrophic and contagious losses. For the modelling of aggregate losses from cyber events, in this paper we introduce a bivariate compound dynamic contagion process, where the bivariate dynamic contagion process is a point process that includes both externally excited joint jumps, which are distributed according to a shot noise Cox process and two separate self-excited jumps, which are distributed according to the branching structure of a Hawkes process with an exponential fertility rate, respectively. We analyse the theoretical distributional properties for these processes systematically, based on the piecewise deterministic Markov process developed by Davis (1984) and the univariate dynamic contagion process theory developed by Dassios and Zhao (2011). The analytic expression of the Laplace transform of the compound process and its moments are presented, which have the potential to be applicable to a variety of problems in credit, insurance, market and other operational risks. As an application of this process, we provide insurance premium calculations based on its moments. Numerical examples show that this compound process can be used for the modelling of aggregate losses from cyber events. We also provide the simulation algorithm for statistical analysis, further business applications and research.

COMPULSORY STATE PENSION INSURANCE WITHIN THE PENSION SECURITY SYSTEM OF UKRAINE

Ukraine has been reforming its pension provision for a long time, and in particular, such an important component as compulsory state pension insurance. The changes that have taken place as a result of these reforms have not yielded adequate results, and serious problems continue to exist regarding the balancing and long-term financial stability of the budget of the Pension Fund of Ukraine. Therefore, the study of the processes taking place in the solidarity system of pension insurance and the search for solutions to problems in this area is extremely relevant. The purpose of the study is to identify trends in the development of compulsory state pension insurance in Ukraine and substantiate its role in providing disabled citizens with adequate pension protection. The article is devoted to the study of the current state of compulsory state pension insurance and substantiation of its role in providing disabled citizens with decent pension benefits. The analysis of incomes, expenses and deficit of the Pension Fund of Ukraine is carried out, their comparison in national and foreign currencies is carried out. It is established that nominal revenues to the Pension Fund of Ukraine and its expenditures tended to increase, but when they were converted into foreign currency there was a decrease in these indicators (except for 2013), which indicates contradictory trends related to the depreciation of income and fund expenses. It has been proven that the Pension Fund of Ukraine constantly lacks its own funds to meet its pension obligations, as a result of which significant budgetary resources are absorbed and the majority of pensioners are not provided with decent pension benefits. Factors influencing the deficit of the Pension Fund of Ukraine have been identified. It is concluded that the problem of low pensions is largely a consequence of the general economic conditions in the country and to a lesser extent - a consequence of the structure or functioning of the solidarity system itself. After all, the basis for calculating insurance premiums is wages, which are low for most employees. Factors that negatively affect the functioning of the state pension insurance have been identified and measures to overcome them have been identified.

A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles

Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process $S$ under a probability measure $P$ we characterize all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ remains a compound renewal process under $Q$. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.

MANAGEMENT OF INTANGIBLE ASSETSS OF THE ENTERPRISE INNOVATIVE PERFORMANCE WITH REFERENCE TO RISKS

The article is devoted to the analysis of existing assessment tools of intangible results of innovative performance that are used to manage the innovative development of the enterprise. The authors consider the most common methods for determining the risk premium when calculating the discount rate. The study shows that existing methods take into account intangible results to a different extent. At the same time, not all intangible results of innovative performance and not in all methods are taken into account properly, this proves that accounting of intangible results can change the discount rate and affect the future cash flows of the enterprise and, as a consequence, the value of the enterprise. Purpose: analysis of existing methods of estimated risk correction development of «factor model for calculating the risk premium» taking into account intangible results of innovative performance. Methods and Methodology: complex of methods of theoretical research (description, comparison, analysis and synthesis), empirical research (expert assessment). Results: development of “factor model for calculating the risk premium taking into account the intangible results of innovation”, which allows more reliable calculation of the risk premium, and as a consequence of the discount rate, which makes it possible to make management decisions reasonably and promptly. Practical implications: It is advisable for economic entities to use the obtained results. That can help them expand the number of analyzed intangible results of innovative activity within the framework of a particular risk factor in order to increase the reliability of calculating the risk premium and, as a result, the discount rate.

Event Data Recorder (EDR) systems in the context of claims adjustment in motor insurance. A case of Poland

The aim of this paper is to present relevant information on EDR (Event Data Recorder) as well as to analyse how EDR systems may be applied within the process of claims adjustment in the Polish motor insurance. Although, neither Polish nor European legislation directly refers to the said systems, their significance is continuously growing. The discussed systems are currently applied within the majority of the newly sold vehicles in Poland. Brand new versions of those systems allow identifying some key circumstances and factors of traffic accidents such as the exact place of an accident, velocity of the vehicle, a number of the people involved or a number of explosions of car air-bag inflators. However, it should be noted that originally the EDR systems primarily were to improve a level of driving safely while the identification of traffic accidents causes was only an additional and marginal benefit. In other words, a question should be posed whether it is admissible under the relevant law regulations that the data recorded in the system may in advance determine a cause of an accident. Other doubts which may result from the EDR are privacy concerns and data ownership as well as the use of the EDR systems within a process of detecting potential fraud or offences related to claims adjustment. For obvious limitation of time and space, premium calculation fells outside the scope of this paper as this particular issue requires separate and detailed considerations.

New Modifications of Express Certificates on Two Assets

The aim of the paper is to focus on modifications of express certificates. The paper shows the creation techniques of a new express certificate using two-asset correlation options and barrier options, which play the central role in financial engineering. Different possibilities of investment are investigated for the issuers and potential investor's point of view. Methodology of the paper is based on European style two-asset correlation options whose payoff is based on two underlying assets with two strike prices and barrier options. Due to the lack of real-traded two asset correlation options and barrier options, own calculations of option premiums are processed in MS Excel and statistical program R.

Livestock mortality catastrophe insurance using fatal shock process

A major problem facing livestock producers is animal mortality risk. Livestock mortality insurance is still at the initial stages, and premium computation approaches are still relatively new and will require more research. We study multi-peril mortality insurance covering the death of livestock in Canada due to a number of natural causes and animal diseases. The coverage includes diseases that must be reported to the CFIA (Canadian Food Inspection Agency). When a Federal reportable disease (FRD) occurs, the CFIA orders the slaughter of animals. A general model to compute premiums, based on actuarial approaches, has been developed for mortality insurance incorporating FRD. This model can be applied to hogs, cattle, and poultry, and is designed to cover all stages of livestock production.Mortality multi-peril insurance premiums are computed for illustration purposes. Hogs are used as an example, specifically in their final 16 weeks (from the 9th week to the 25th week) when they weigh between 23 kg to 113 kg. This is referred to as the third stage (cycle) or the finishing/grower stage. Premium estimates are generated based on the mortality data. In addition, an additional CFIA reportable disease not seen in the data is assumed. However, it is assumed that producers receiving animal mortality compensation from the CFIA would have their mortality insurance indemnity payouts reduced by the amount of the CFIA animal compensation (no double collection of funds by producers). We introduce fatal shock processes to incorporate the CFIA reportable disease. Having these shocks, all hogs raised in the same farm are facing the same fate with FRD since all hogs will be slaughtered when it occurs. Mortality data is obtained from a North American sample from 1999–2007, covering 139 million hog-months over a number of monthly periods. We calculate premium rate based on per 1,000 hogs raised in the same farm with modifications including deductible and coverage level.

Long term care insurance pricing in Spanish population: a functional data approach

Developed and developing countries are experiencing the consequences of an ever-increasing elderly population, including the challenges of chronic illness, disability, dependency and long term care. All over the world, more people are surviving diseases that were fatal some decades ago. Dependency can be seen as a consequence of the process of gradual aging. In a health context, this contingency is defined as a lack of autonomy in performing basic activities of daily living that requires the care of another person or significant help. In this work we propose a stand-alone insurance, focused on the necessities of the eligible dependent people in Spain, taking into account their health evolution along their lives, in order to enhance the net premium calculation. We use information from the Spanish survey EDAD 2008. The main finding is that, a policyholder can choose to underwrite among three kinds of coverages, going from a minimum to a maximum level of protection, the latter's premium being more than twice the former's, regardless of the onset of dependency.

Comparison of the costs of the defined-benefit and the defined-contribution schemes under an actuarial methodology

El objetivo de este trabajo es utilizar herramientas básicas de análisis actuarial para demostrar por primera vez que el costo del financiamiento del esquema de beneficio-definido es igual al de un esquema de contribución-definida siempre que estos planes otorguen beneficios iguales en términos de cantidad y condiciones para obtenerlos, y llevamos a cabo nuestros cálculos usando las mismas hipótesis financieras y biométricas. Enunciamos nuestros resultados en términos de un cálculo individual y de un modelo grupal (en el segundo caso, el esquema de beneficio definido requiere del cómputo de una prima media general); y en ambos escenarios, estudiamos la posibilidad de la jubilación anticipada con portabilidad total y parcial. Nuestra recomendación general es abandonar el debate sobre qué esquema es más caro. La principal limitante de nuestra investigación es también su mayor fortaleza: hemos demostrado que no hay predominio de ninguno de los planes sobre el otro cuando no hay otras distorsiones del mercado laboral; lo que significa que la discusión podría continuar vigente si consideramos la presencia de tales factores.

Impact De-Tarrification in Modeling Motor Insurance Premium in Malaysia

De-tariffication has become a hot topic for Malaysian motor insurers after effectively implemented on 1 July 2017. Generally, the insurance companies need to set a rating factor for their premium before calculating the price on selected premium. Typically, these rating factors are based on the risk profile of the policyholder. That means, the price of the premium determined by the risk factors from the profile of the policyholder. The aim of this research to investigate the impact after de-tariff implemented among the motor insurance industry. This research also investigates the effect of de-tariff on the Good Service Tax (GST) in the premium calculation. Multiple Linear Regression (MLR) was used to determine the most significant rating factor that influence the calculation of the premium received by the motor insurance industry. Once these k rating factors and parameters are identified, the value of premiums can be calculated by taking into account these rating factors and parameters in the de-tariff formula and comparing with the existing model. The result of the study indicates that de-tariff model has lower premium compared to Malaysia tariff model. Furthermore, GST is also found to have a significant impact on the motor insurance premium, where policyholders are required to pay higher premiums than non-GST premiums. The results will help the insurance companies to find new formulas in considering new rating factors and improve the accuracy of premium calculations.

Pricing of Premium for Automobile Insurance using Bayesian Method

The aggregate claim model can be used to determine the amount of premium charged to the insured by the insurance company. This model consists of two mutually independent random variables, namely the number of claims that occur per period and the amount of claim for each event. In this study, the number of claims is Poisson distributed, and the amount of claim is distributed by generalized extreme value (GEV). The Bayes method is used to estimate the parameters of each distribution. Parameter estimation results are used to calculate the expectations and variances of the aggregate claim model which are then used to calculate insurance premiums. Based on the estimation results, the amount of premium charged to the insured ranges from IDR 3,831,480 to IDR 6,443,860.

Weak comonotonicity

The classical notion of comonotonicity has played a pivotal role when solving diverse problems in economics, finance, and insurance. In various practical problems, however, this notion of extreme positive dependence structure is overly restrictive and sometimes unrealistic. In the present paper, we put forward a notion of weak comonotonicity, which contains the classical notion of comonotonicity as a special case, and gives rise to necessary and sufficient conditions for a number of optimization problems, such as those arising in portfolio diversification, risk aggregation, and premium calculation. In particular, we show that a combination of weak comonotonicity and weak antimonotonicity with respect to some choices of measures is sufficient for the maximization of Value-at-Risk aggregation, and weak comonotonicity is necessary and sufficient for the Expected Shortfall aggregation. Finally, with the help of weak comonotonicity acting as an intermediate notion of dependence between the extreme cases of no dependence and strong comonotonicity, we give a natural solution to a risk-sharing problem.

An Individual Risk Model for Premium Calculation Based on Quantile: A Comparison between Generalized Linear Models and Quantile Regression

This article deals with the use of quantile regression and generalized linear models for a premium calculation based on quantiles. A premium principle is a functional that assigns a usually loaded premium to any distribution of claims. The loaded premium is generally greater than the expected value of the loss and the difference is considered to be a risk margin or a safety loading. The failure of a right charge of individual risk rate exposes the insurer to adverse selection and, consequently, to deteriorating financial results. The article aim is to define the individual pure premium rates and the corresponding risk margin in balance with some profit or solvency constraints. We develop a ratemaking process based on a two-part model using quantile regression and a gamma generalized linear model, respectively, in order to estimate the claim’s severity quantiles. Generalized linear models focus on the estimation of the mean of the conditional loss distribution but have some drawbacks in assessing distribution moments other than the mean and are very sensitive to outliers. On the contrary, quantile regression exceeds these limits leading to the estimate of conditional quantiles and is more accurate for a better measurement of the variability of a risk class. The proposed methodology for premium calculation allows us to find further limits of the generalized linear model as the solution we found, under specific assumptions for a generalized linear model, is equivalent to the application of the expected value premium principle. Finally, the methodology we suggest for the two-part quantile regression allows reducing the practical issue of overmodeling and over-parameterization with respect to other proposals on the same topic.

Model of Rice Farm Insurance to Reduce Losses Due to Harvest Failure

The rice farm insurance is one of micro insurance, which is intended for paddy fields. Its use is to reduce or minimize the losses suffered by farmers due to crop failure. In this article various things are related to rice farming insurance and specifically highlight rice farming insurance in Indonesia from the actuarial side. There are several actuarial methods that can be used to determine the amount of rice farming insurance premiums. Calculation of premiums is based on expectations of losses and losses of extreme events. The premium calculation used is: pure premium method, and method of level of coverage. Based on the results of the discussion, it shows that the actuarial fair premium determined in the range of IDR 179,000 to IDR 268,000. Thus, the official premium of rice farming insurance is IDR 180,000, is the minimum premium for agricultural insurance programs in Indonesia.

PERHITUNGAN PREMI DENGAN PENERAPAN DEDUCTIBLE PADA MODEL AKTUARIA UNTUK SICKNESS INSURANCE PERTANGGUNGAN SATU TAHUN

Health insurance is an insurance product that provides benefits if the insured is exposed to the risk of an accident or illness and causes loss of income, thus requiring costs. The most important benefit in this study from sickness insurance is the reimbursement of medical expenses. The design of determining premiums by applying deductibles (flat deductibles) is seen as one of the insurance policy policies that meet the principles of determining premiums. The actuarial aspects considered in the health insurance model in this study for the calculation of premiums relating to the type of insurance benefits with expense reimbursement for a period of one year coverage, with due regard to the type of work. The purpose of this study is to see the applied of deductible to the premiums that must be paid to insurance companies that provide benefits for claims submitted. The policy of applying deductibles certainly makes the amount of reimbursement change.

Joint life insurance based on Gompertz assumptions and interest rate affected by the excange rate

This paper discussed about Calculation of joint life insurance premiums based on Gompertz mortality assumptions that affect the probability of joint insurance participants. One important variable in calculating premiums and reserves is interest rates. The foreign exchange rate is the price of a currency if exchanged with another countrys currency. Depreciation in the foreign exchange rate causes fluctuations in interest rates which ultimately affect the calculation of premiums for joint life insurance. Based on the calculation results, the greater the depreciation value, the greater the interest rate. This will increase risk for insurance companies. Calculation of insurance premiums that are affected by dollar fluctuations, is expected to be able to obtain calculations that are in accordance with the world economic trends.

Heterogeneity in mortality: a survey with an actuarial focus

Heterogeneity in mortality is due to differences among the individuals, which are caused by various risk factors. Some risk factors are observable while others are unobservable. The set of observable risk factors clearly depends on the type of population addressed. The impact of observable risk factors on individual mortality, in particular when they also constitute “rating factors” in the calculation of premiums and other actuarial values, is usually expressed approximately, according to some pragmatic approach. For example, additive or multiplicative adjustments to the average age-specific mortality are frequently adopted. Heterogeneity due to unobservable risk factors can conversely be expressed by adopting the concept of individual “frailty”, which, however, can be interpreted and consequently modeled in several ways, according to the causes which are considered as originating the frailty itself: congenital characteristics, environmental features, lifestyle aspects, etc. In this paper, we provide a survey of scientific contributions on heterogeneity in mortality, focusing on modeling both observable and unobservable heterogeneity. We start with an overview of methodological contributions to heterogeneity and frailty modeling, coming from both the demographical and the actuarial context. We then shift to contributions analyzing the impact of frailty, in its various interpretations, on the results (cash flows, profits, etc.) of life insurance and life annuity portfolios and related risk profiles.