Elasticity as a Means of Evaluating Bonus-Malus Systems in Automobile Insurance

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dc.contributor Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta fi
dc.contributor University of Helsinki, Faculty of Science en
dc.contributor Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten sv
dc.contributor.author Virri, Maria
dc.date.issued 2021
dc.identifier.uri URN:NBN:fi:hulib-202106082550
dc.identifier.uri http://hdl.handle.net/10138/330733
dc.description.abstract Bonus-malus systems are used globally to determine insurance premiums of motor liability policy-holders by observing past accident behavior. In these systems, policy-holders move between classes that represent different premiums. The number of accidents is used as an indicator of driving skills or risk. The aim of bonus-malus systems is to assign premiums that correspond to risks by increasing premiums of policy-holders that have reported accidents and awarding discounts to those who have not. Many types of bonus-malus systems are used and there is no consensus about what the optimal system looks like. Different tools can be utilized to measure the optimality, which is defined differently according to each tool. The purpose of this thesis is to examine one of these tools, elasticity. Elasticity aims to evaluate how well a given bonus-malus system achieves its goal of assigning premiums fairly according to the policy-holders’ risks by measuring the response of the premiums to changes in the number of accidents. Bonus-malus systems can be mathematically modeled using stochastic processes called Markov chains, and accident behavior can be modeled using Poisson distributions. These two concepts of probability theory and their properties are introduced and applied to bonus-malus systems in the beginning of this thesis. Two types of elasticities are then discussed. Asymptotic elasticity is defined using Markov chain properties, while transient elasticity is based on a concept called the discounted expectation of payments. It is shown how elasticity can be interpreted as a measure of optimality. We will observe that it is typically impossible to have an optimal bonus-malus system for all policy-holders when optimality is measured using elasticity. Some policy-holders will inevitably subsidize other policy-holders by paying premiums that are unfairly large. More specifically, it will be shown that, for bonus-malus systems with certain elasticity values, lower-risk policy-holders will subsidize the higher-risk ones. Lastly, a method is devised to calculate the elasticity of a given bonus-malus system using programming language R. This method is then used to find the elasticities of five Finnish bonus-malus systems in order to evaluate and compare them. en
dc.language.iso eng
dc.publisher Helsingin yliopisto fi
dc.publisher University of Helsinki en
dc.publisher Helsingfors universitet sv
dc.subject Bonus-malus systems
dc.subject automobile insurance
dc.subject Markov chains
dc.subject elasticity
dc.title Elasticity as a Means of Evaluating Bonus-Malus Systems in Automobile Insurance en
dc.type.ontasot pro gradu -tutkielmat fi
dc.type.ontasot master's thesis en
dc.type.ontasot pro gradu-avhandlingar sv
dct.identifier.urn URN:NBN:fi:hulib-202106082550
dc.subject.specialization Sovellettu matematiikka fi
dc.subject.specialization Applied Mathematics en
dc.subject.specialization Tillämpad matematik sv
dc.subject.degreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi
dc.subject.degreeprogram Master's Programme in Mathematics and Statistics en
dc.subject.degreeprogram Magisterprogrammet i matematik och statistik sv

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