scholarly journals Calculating Premium Credibility Using the Buhlmann-Straub Modelwith Nonparametric Assessment

2020 ◽  
Vol 1 (1) ◽  
pp. 20-32
Author(s):  
Dwi Susanti ◽  
Sokono Sukono
Keyword(s):  
Nonparametric Estimation ◽  
Total Loss ◽  
Credibility Theory ◽  
Risk Level ◽  
Individual Risk ◽  
Claim Amount ◽  
Insurance Company ◽  
Data Set ◽  
General Insurance ◽  
The Individual

When an insurance company calculates the premium it will divides the policy holders into groups. The division is considered based on risk level in each group. The problem is then to devise a way of combining the experience risk of the group with the experience of the individual risk to calculate the premium, so then Credibility Theory provides a solution to this problem.This script discuss about calculation of credibility premium use Buhlmann-Straub Model with nonparametric estimation to the aggregate claim amount data set within few years observation in some group of policy holders in  general insurance. By using credibility theory we can calculate the value of credibility factor and credibility premium or future premium. The value of premium credibility is calculated from only one group of policyholders from the previous year's data. For better value of premium credibility, data with more experience years and the policyholder group better reflect the total loss value during the observation year.The result of this calculation are credibility factor per group, average credibility premium per members in group and credibility premium total for the last year for each group. We can obtain total losses and total premium which surprisingly equal. 

Determinants of United Kingdom General Insurance Company Performance

2004 ◽  
Vol 10 (5) ◽  
pp. 1079-1110 ◽  
Author(s):  
Y. Shiu
Keyword(s):  
United Kingdom ◽  
Panel Data ◽  
Performance Measures ◽  
Panel Data Analysis ◽  
Ordinary Least Squares ◽  
Insurance Companies ◽  
Company Performance ◽  
Insurance Company ◽  
Data Set ◽  
General Insurance

ABSTRACTDynamic financial analysis has become one of the important tools that actuaries use to model the underwriting and investment operations of insurance companies. The first step in carrying out the analysis is to investigate the most important factors affecting company performance. This paper identifies the determinants of the performance of United Kingdom general insurance companies using a panel data set consisting of economic data and Financial Services Authority/Department of Trade and Industry returns over the period 1986 to 1999. Three performance measures are used to capture different aspects of insurance operations. These measures are related to a number of economic and firm specific variables, chosen on the basis of relevant theory and literature. An ordinary least squares regression model and two panel data models are estimated for each of three performance measures. This paper also addresses several important econometric problems that are usually ignored in applied work in the context of panel data analysis. Based on the empirical results, this study finds that liquidity, unexpected inflation, interest rate level and underwriting profits are statistically significant determinants of the performance of U.K. general insurers.

scholarly journals A Functional Approach to Approximations for the Individual Risk Model

2004 ◽  
Vol 34 (2) ◽  
pp. 379-397 ◽  
Author(s):  
Susan M. Pitts
Keyword(s):  
Negative Binomial ◽  
Risk Model ◽  
Order Approximation ◽  
Functional Approach ◽  
Individual Risk ◽  
Claim Amount ◽  
Total Claim Amount ◽  
Total Claim ◽  
Binomial Approximation ◽  
The Individual

A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.

scholarly journals Prediction of Outstanding Liabilities in Non-Life Insurance

1993 ◽  
Vol 23 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Ragnar Norberg
Keyword(s):  
Life Insurance ◽  
Linear Prediction ◽  
Basic Result ◽  
Claim Amount ◽  
Insurance Company ◽  
Life Insurance Company ◽  
Total Claim Amount ◽  
Generalized Poisson ◽  
Total Claim ◽  
The Individual

AbstractA fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.

scholarly journals Financial Market and Inflation

2020 ◽  
Vol 12 (6) ◽  
pp. 90
Author(s):  
Yuqing Qi
Keyword(s):  
Systemic Risk ◽  
Predictive Accuracy ◽  
Predictive Ability ◽  
Two Dimensions ◽  
Risk Indicators ◽  
Risk Level ◽  
Individual Risk ◽  
Inflation Risk ◽  
The Future ◽  
The Individual

Based on two dimensions of system risk, this paper studies the changes in the future inflation risk level, and uses the out-of-sample quantile R2  to further evaluate the predictive accuracy of different systemic risk indicators on inflation risk. Firstly, we compute two systemic risk indicators, MES and volatility, with data of Chinese financial institutions. And then we explore the amplification effect of these indicators on future inflation risk, under the framework of quantile regression. We find that systematic risk indicators have a strong predictive ability for the inflation level at various quantiles. MES indicator that reflects individual risk can better predict future deflation risk, while volatility index has a stronger ability to predict inflation risk. We also find that systemic risk indicators of different dimensions have different effects on inflation risk and deflation risk. In general, the MES index, which captures the individual risk of the organization, have a greater impact on the future inflation risk. While indicator that measures volatility in financial markets has more influence on the extreme lower tail of inflation rates. Finally, we predict the distribution of inflation in China from March 2020 to June 2021, and visually show the distribution trend of future inflation with forecast fan charts.

scholarly journals Late Reinfection With a Different SARS-CoV-2 Clade in a Patient With Refractory Arterial Hypertension: a Case Report.

2021 ◽  
Author(s):  
Antonio Galiana ◽  
Javier García-Abellán ◽  
Marta Fernández-González ◽  
Nieves Gonzalo-Jiménez ◽  
Montserrat Ruiz-García ◽  
...  
Keyword(s):  
Arterial Hypertension ◽  
Primary Infection ◽  
Individual Risk ◽  
Time Interval ◽  
Limited Information ◽  
Data Set ◽  
Initial Infection ◽  
Viral Shedding ◽  
The Individual

Abstract Background: Differentiating between persistent infection with intermittent viral shedding and reinfection with SARS-CoV-2 remains challenging. Although a small number of cases with genomic evidence of second infection have been reported, limited information exists on frequency and determinants of reinfection, time between infections, and duration of immunity after the primary infection. Case presentation: We report a reinfection with SARS-CoV-2 in a 52-year old male whose primary infection was diagnosed in May 2020, during the first wave of the pandemic in Spain, and the second occurred eight months later, in January 2021. We present a complete data set including results from real-time polymerase chain reaction, serology and genome sequencing confirming reinfection with a different clade. Noteworthy was that the patient was immunocompetent but had multiple cardiometabolic comorbidities, including refractory arterial hypertension, that might increase the individual risk in COVID-19.Conclusions: This case of reinfection with SARS CoV-2 occurring several months after the primary infection reports the longest time interval between reinfection and initial infection described to date. It raises concerns on the duration of protective immunity, suggesting that it may begin to wane in patients who acquired the initial infection during the first wave of the pandemic. The potential contributing role of arterial hypertension and cardiometabolic comorbidities as risk factors for reinfection deserves investigation.

scholarly journals A Functional Approach to Approximations for the Individual Risk Model

2004 ◽  
Vol 34 (02) ◽  
pp. 379-397 ◽  
Author(s):  
Susan M. Pitts
Keyword(s):  
Negative Binomial ◽  
Risk Model ◽  
Order Approximation ◽  
Functional Approach ◽  
Individual Risk ◽  
Claim Amount ◽  
Total Claim Amount ◽  
Total Claim ◽  
Binomial Approximation ◽  
The Individual

A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.

scholarly journals Risk to life due to flooding in post-Katrina New Orleans

2015 ◽  
Vol 15 (1) ◽  
pp. 59-73 ◽  
Author(s):  
A. Miller ◽  
S. N. Jonkman ◽  
M. Van Ledden
Keyword(s):  
Hurricane Katrina ◽  
New Orleans ◽  
Flood Risk ◽  
Large Scale ◽  
Central Area ◽  
Protection System ◽  
Risk Level ◽  
Individual Risk ◽  
Loss Of Life ◽  
The Individual

Abstract. Since the catastrophic flooding of New Orleans due to Hurricane Katrina in 2005, the city's hurricane protection system has been improved to provide protection against a hurricane load with a 1/100 per year exceedance frequency. This paper investigates the risk to life in post-Katrina New Orleans. In a flood risk analysis the probabilities and consequences of various flood scenarios have been analyzed for the central area of the city (the metro bowl) to give a preliminary estimate of the risk to life in the post-Katrina situation. A two-dimensional hydrodynamic model has been used to simulate flood characteristics of various breaches. The model for estimation of fatality rates is based on the loss of life data for Hurricane Katrina. Results indicate that – depending on the flood scenario – the estimated loss of life in case of flooding ranges from about 100 to nearly 500, with the highest life loss due to breaching of the river levees leading to large flood depths. The probability and consequence estimates are combined to determine the individual risk and societal risk for New Orleans. When compared to risks of other large-scale engineering systems (e.g., other flood prone areas, dams and the nuclear sector) and acceptable risk criteria found in literature, the risks for the metro bowl are found to be relatively high. Thus, despite major improvements to the flood protection system, the flood risk to life of post-Katrina New Orleans is still expected to be significant. Indicative effects of reduction strategies on the risk level are discussed as a basis for further evaluation and discussion.

Conditional mean risk sharing in the individual model with graphical dependencies

2021 ◽  
pp. 1-27
Author(s):  
Michel Denuit ◽  
Christian Y. Robert
Keyword(s):  
Graphical Models ◽  
Risk Sharing ◽  
Risk Model ◽  
Allocation Rule ◽  
Individual Risk ◽  
Claim Amount ◽  
Conditional Mean ◽  
Operational Risks ◽  
The Individual ◽  
Mean Risk

Abstract Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.

scholarly journals Risk to life due to flooding in post-Katrina New Orleans

2014 ◽  
Vol 2 (1) ◽  
pp. 825-864 ◽  
Author(s):  
A. Miller ◽  
S. N. Jonkman ◽  
M. Van Ledden
Keyword(s):  
Hurricane Katrina ◽  
New Orleans ◽  
Large Scale ◽  
Central Area ◽  
Protection System ◽  
Risk Level ◽  
Individual Risk ◽  
Loss Of Life ◽  
Reduction Strategies ◽  
The Individual

Abstract. After the catastrophic flooding of New Orleans due to hurricane Katrina in the year 2005, the city's hurricane protection system has been improved to provide protection against a hurricane load with a 1/100 per year exceedance frequency. This paper investigates the risk to life in post-Katrina New Orleans. In a risk-based approach the probabilities and consequences of various flood scenarios have been analyzed for the central area of the city (the metro bowl) to give a preliminary estimate of the risk to life in the post-Katrina situation. A two-dimensional hydrodynamic model has been used to simulate flood characteristics of various breaches. The model for estimation of fatality rates is based on the loss of life data for Hurricane Katrina. Results indicate that – depending on the flood scenario – the estimated loss of life in case of flooding ranges from about 100 to nearly 500, with the highest life loss due to breaching of the river levees leading to large flood depths. The probability and consequence estimates are combined to determine the individual risk and societal risk for New Orleans. When compared to risks of other large scale engineering systems (e.g. other flood prone areas, dams and the nuclear sector) and acceptable risk criteria found in literature, the risks for the metro bowl are found to be relatively high. Thus, despite major improvements to the flood protection system, the flood risk of post-Katrina New Orleans is still expected to be significant. Effects of reduction strategies on the risk level are discussed as a basis for further evaluation.

scholarly journals Experience Rating with Credibility Adjustment of the Manual Premium

1974 ◽  
Vol 7 (3) ◽  
pp. 323-336 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Stage I ◽  
Individual Risk ◽  
Claim Amount ◽  
Common Procedure ◽  
Experience Rating ◽  
The Common ◽  
The Individual ◽  
Two Stages

AbstractA common procedure for experience rating is to use Whitney's credibility formula with the manual premium per risk unit estimated by the observed average claim amount per risk unit. As pointed out by Whitney himself, this observed average also needs to be subjected to credibility adjustment. This suggestion is pursued in the paper and an experience rating procedure developed in which there are two stages:(i) revision of the prior expected manual premium in accordance with the observed average claim amount per risk unit;(ii) experience rating of the individual risk classes by the usual methods but using the manual premium obtained in stage (i).Both stages of this procedure involve credibility indices, for which formulae are developed.Conditions under which the “common procedure” referred to above is fairly reliable are found and it is seen, somewhat surprisingly, that the procedure is often more valid than one expects on intuitive grounds. Care is necessary, however, when there are wide differences in size between different risk classes.

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