scholarly journals The Application of Bühlmann‑Straub Model with Data Correction for the Estimation of Net Premium Rates in Bonus‑Malus Systems of the Motor Third Liability Insurance

2018 ◽  
Vol 4 (336) ◽  
pp. 7-22
Author(s):  
Anna Edyta Szymańska
Keyword(s):  
Estimation Method ◽  
Third Party ◽  
Liability Insurance ◽  
New Method ◽  
Insurance Companies ◽  
Data Correction ◽  
Insurance Portfolio ◽  
Premium Rates ◽  
The Right

One of the elements used in the process of tariff calculation of premiums in motor liability insurance is a bonus‑malus system. This systems takes into account the “claims ratio” by means of increases and discounts of the base premium called net premium rates. The aim of this work is to propose an estimation method of the net premium rates in the bonus‑malus classes of the motor third‑party liability insurance portfolio of individuals. The Bühlmann‑Straub model was used for the premium estimation. In order to improve the credibility of the estimated premium rates, a data correction in the classes with premium increase was preformed. An example of the application of the new method is presented based on the data obtained from one of the insurance companies operating on the Polish market, which has reserved the right to stay anonymous.

scholarly journals The Application of Bühlmann-Straub Model to the Estimation of Net Premium Rates Depending on the Age of the Insured in the Motor Hull Liability Insurance

2016 ◽  
Vol 3 (322) ◽  
Author(s):  
Anna Szymańska
Keyword(s):  
Maximum Likelihood ◽  
Liability Insurance ◽  
Rate Estimation ◽  
Insurance Portfolio ◽  
Premium Rates

One of the basic variables used in the process of tariff calculation of premiums in motor hull liability insurance is the age of the insured. In this type of insurance offered by insurers operating on the Polish market, this variable is taken into account in the ratemaking by discounts and increases in assigned premium, known as the net premiums rates. The aim of this work is to propose a method of rate estimation of net premiums in the groups of the motor hull liability insurance portfolio of individuals created by the age of the insured. For the premium estimation one of the maximum likelihood models, called the Bühlmann-Straub model was used.

scholarly journals On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study

Risks ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 71 ◽  
Author(s):  
Marjan Qazvini
Keyword(s):  
Poisson Regression ◽  
Third Party ◽  
Liability Insurance ◽  
Insurance Pricing ◽  
Excess Zeros ◽  
Insurance Portfolio ◽  
Zip Model ◽  
Validation Set ◽  
Insurance Data ◽  
Better Than

In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that how the type of coverage and policyholders’ willingness to subscribe to insurance pricing, based on telematics data, affects their driving behaviour and hence their claims. Using our validation set, we then predict the number of zero claims. Our results show that although a zero-inflated Poisson (ZIP) model performs better than a Poisson regression, it can even be outperformed by logistic regression.

scholarly journals The First Liability Insurance Cartel in America, 1896–1906

2011 ◽  
Vol 29 (2) ◽  
pp. 375-417
Author(s):  
Sachin S. Pandya
Keyword(s):  
United States ◽  
The United States ◽  
Liability Insurance ◽  
Insurance Companies ◽  
Personal Injury ◽  
Tort Liability ◽  
Business Operations ◽  
Premium Rates ◽  
Share Information

This article studies the rise and fall of the first liability insurance cartel in the United States. In 1886, insurance companies in America began selling liability insurance for personal injury accidents, primarily to cover business tort liability for employee accidents at work and non-employee injuries occasioned by their business operations. In 1896, the leading liability insurers agreed to fix premium rates and share information on policyholder losses. In 1906, this cartel fell apart.

scholarly journals CURRENT STATE OF REGIONAL INSURANCE BY THE EXAMPLE OF THE KEMEROVO REGION

2017 ◽  
Vol 2017 (1) ◽  
pp. 39-46
Author(s):  
Ольга Козлова ◽  
Olga Kozlova
Keyword(s):  
Third Party ◽  
Insurance Market ◽  
Insurance Companies ◽  
Insurance Risk ◽  
Current State ◽  
Insurance Portfolio ◽  
Compulsory Insurance ◽  
Hazardous Production ◽  
Car Insurance

<p>The article considers the current state of insurance market in the Kemerovo region, as well as trends affecting the market. In the crisis year of 2015, the insurance market of Russia and Kemerovo region was developing due to the growth of compulsory insurance and life insurance, whereas classical insurance saw a decline. Comparative analysis of insurance market in Russia showed a preferential development of optional medical insurance and compulsory third party car insurance in the regional insurance market. The article features an analysis of the structure of the insurance portfolio of the regional insurance companies, the place and the role of the regional insurance companies in the insurance market of the Kemerovo region. Regional insurance organizations specialize in voluntary health insurance, which reflects the specifics of the regional insurance risk, but its overall development is not steady, without regard to regional peculiarities. Conclusions are drawn about the lack of a regional perspective, the need for the development of regional insurance, since regional insurance organizations are able to take into account the specifics of the site and agree to cover relevant risks. An example is the compulsory insurance of civil liability of owners of hazardous production facilities, where a significant role belongs to the regional insurance organizations.</p>

scholarly journals PROSPECTS FOR THE DEVELOPMENT OF MOTOR THIRD PARTY LIABILITY INSURANCE ON THE BULGARIAN INSURANCE MARKET

2019 ◽  
Vol 17 (Suppl.1) ◽  
pp. 480-487
Author(s):  
Tzvetelina Andreeva
Keyword(s):  
Quantitative Methods ◽  
Third Party ◽  
Liability Insurance ◽  
Insurance Market ◽  
Market Development ◽  
Local Market ◽  
Analysis And Evaluation ◽  
Insurance Portfolio ◽  
European Insurance

The aim of the report is to examine the current and important for the society issues concerning one of the most widespread insurance products - Motor Third Party Liability Insurance. The report examines the use of Motor Third Party Liability insurance on our insurance market. Specific studies have been made on the actual presence of the insurance in the local market and the motor insurance in the general insurance portfolio at European level. The problems and trends in the application and the proposed "Bonus-Malus" system are considered. Further considerations regarding the Bonus-Malus system have been made, taking into account the role of the system for fair payment of insurance premiums. The positive experience of the European insurance market is also reported. The report also focuses on other regulatory and other factors determining the market development. Quantitative methods of analysis and evaluation are used.

JOINT OPTIMIZATION OF TRANSITION RULES AND THE PREMIUM SCALE IN A BONUS-MALUS SYSTEM

2020 ◽  
Vol 50 (3) ◽  
pp. 743-776
Author(s):  
Kolos Csaba Ágoston ◽  
Márton Gyetvai
Keyword(s):  
Mixed Integer Linear Programming ◽  
Third Party ◽  
Liability Insurance ◽  
Insurance Companies ◽  
Mixed Integer ◽  
Joint Optimization ◽  
Transition Rules ◽  
Number Of Classes ◽  
Stationary Probabilities

AbstractBonus-malus systems (BMSs) are widely used in actuarial sciences. These systems are applied by insurance companies to distinguish the policyholders by their risks. The most known application of BMS is in automobile third-party liability insurance. In BMS, there are several classes, and the premium of a policyholder depends on the class he/she is assigned to. The classification of policyholders over the periods of the insurance depends on the transition rules. In general, optimization of these systems involves the calculation of an appropriate premium scale considering the number of classes and transition rules as external parameters. Usually, the stationary distribution is used in the optimization process. In this article, we present a mixed integer linear programming (MILP) formulation for determining the premium scale and the transition rules. We present two versions of the model, one with the calculation of stationary probabilities and another with the consideration of multiple periods of the insurance. Furthermore, numerical examples will also be given to demonstrate that the MILP technique is suitable for handling existing BMSs.

scholarly journals Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System

1999 ◽  
Vol 29 (2) ◽  
pp. 327-337 ◽  
Author(s):  
Meng Shengwang ◽  
Yuan Wei ◽  
G.A. Whitmore
Keyword(s):  
Pareto Distribution ◽  
Negative Binomial ◽  
Poisson Model ◽  
Bayes Theorem ◽  
Third Party ◽  
Liability Insurance ◽  
Automobile Insurance ◽  
Individual Level ◽  
Insurance Portfolio ◽  
Over Dispersion

AbstractIndividual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).

scholarly journals Subrogation in the Rear-View: Evaluating Alberta's Current Approach to Automobile Liability Insurance for Impaired Drivers

2014 ◽  
Vol 51 (3) ◽  
pp. 601
Author(s):  
Kendal Gummer
Keyword(s):  
Public Policy ◽  
Current System ◽  
Current Approach ◽  
Third Parties ◽  
Third Party ◽  
Liability Insurance ◽  
Previous Approach ◽  
The Public ◽  
Policy Objectives ◽  
The Right

In Alberta, automobile insurers are required to indemnify an insured up to policy limits for injury or property damage to third parties for which the insured is liable. Prior to 1 June 1982, insurers could demand reimbursement for third party liability payments if the insured driver caused loss while under the influence of drugs or alcohol. However, the Insurance Amendment Act removed the right of insurers to recover these sums. This article evaluates this amendment by considering its impact on the public policy objectives ordinarily associated with subrogation, and argues that, compared to the previous approach, Alberta’s current system of third party liability coverage better serves the objectives of subrogation.

scholarly journals Optimal Bonus-Malus System Design in Motor Third-Party Liability Insurance in Turkey: Negative Binomial Model

2016 ◽  
Vol 8 (8) ◽  
pp. 205 ◽  
Author(s):  
Serpil Ergün Bülbül ◽  
Kemal B. Baykal
Keyword(s):  
Financial Stability ◽  
Negative Binomial ◽  
Negative Binomial Model ◽  
Third Party ◽  
Liability Insurance ◽  
Credibility Theory ◽  
Insurance Companies ◽  
Binomial Model ◽  
Insurance Company ◽  
System Data

One of the most significant instruments used in motor third-party liability insurance rating is bonus-malus system. The aim of the bonus-malus system is to provide a fairness of the premiums paid by ensuring everyone pays a premium that corresponds exactly to their own claim frequency. A balance of total amount of bonuses and maluses is very important to maintain the financial stability of the insurance companies. In Turkey, free tariff regime in motor third-party liability insurance has been adopted since 2014. In this study, an experience rating was employed via the insured’s individual claim experience by considering the drawbacks of using mandatory bonus-malus system. Data entailing information about the claim frequencies of automobiles over a year for motor third party liability policies were obtained from an insurance company. Optimal bonus-malus rates are determined by negative binomial model by using credibility theory, Bayesian approach and the principle of expected value premium.

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