Generalized Bonus-Malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance

Mahmoudvand, Rahim; Hassani, Hossein

doi:10.2143/ast.39.1.2038066

Cited by 22 publications

(25 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Anyway (12) must hold. Firstly, we check if it is possible to penalize only claims of type m. To this end, we set d s,0 = d s,1 = · · · = d s,m−1 = 0, d s,m = c * m and substitute this into (12). If…”

Section: Remark 2 Equationmentioning

confidence: 99%

See 1 more Smart Citation

Bonus–malus systems with different claim types and varying deductibles

Ragulina

2017

Modern Stoch. Theory Appl.

View full text Add to dashboard Cite

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bonus-malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus-malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.

show abstract

Section: Remark 2 Equationmentioning

confidence: 99%

“…we also have to penalize at least claims of type m − 1. We set d s,0 = d s,1 = · · · = d s,m−2 = 0, d s,m−1 = c * m−1 , d s,m = c * m and substitute this into (12). If…”

Section: Remark 2 Equationmentioning

confidence: 99%

Bonus–malus systems with different claim types and varying deductibles

Ragulina

2017

Modern Stoch. Theory Appl.

View full text Add to dashboard Cite

show abstract

“…Although there exist many variations of this type of models [21], [22], [23], most of them can be modeled by means of discrete-time Markov chains [24]. The model behind the simulator is a simple version that contains the main features of a BMS.…”

Section: A the Bms Modelmentioning

confidence: 99%

Application of a Discrete-time Markov Chain Simulation in Insurance

Morales

2015

Int. J. Recent Contrib. Eng. Sci. IT

View full text Add to dashboard Cite

Abstract-This paper describes the application of an online interactive simulator of discrete-time Markov chains to an automobile insurance model. Based on the D3.js library, an interactive visual animation depicts the dynamics of individual policyholders in a bonus-malus system of automobile insurance. A survey was conducted among MSc students who used the simulator to obtain a preliminary assessment of the perceived usefulness in several dimensions of their learning process. The main findings indicate that flexible access via different devices was the most valued feature of this resource. In addition, the possibility of experimenting and simulating by means of controlling the main parameter of the model was also found to be particularly useful.

show abstract

“…where GBM F denotes the generalized BMS obtained when only the frequency component is used and GBM S denotes the generalized BMS obtained when only the severity component is used, see also Mahmoudvand and Hassani (2009). It is popular in the BMS literature to use Bayes theory for finding GBM F and GBM S .…”

Section: Introductionmentioning

confidence: 99%