Sistema de bônus malus aplicando a programação dinâmica

Abstract

In this work, a study is made of a stochastic dynamic programming model, in which an accident is considered, an unforeseen or fortuitous event which results in damage to the thing or person. Initially, insurance is described as a means of defense against any type of risk, until the emergence of the malus bonus systems as well as their elementary characteristics, followed by some examples that help to better understand them. An approach is made of the main characteristics and some definitions of Markov chains that are important to clearly understand the transition between the classes of the system. Deterministic and stochastic dynamic programming models are defined and an approach is made in terms of actions and policies. Some theorems on cost minimization and maximization are presented, as well as on the structural properties of the solution of a dynamic program. Finally, a model of a malus bonus system is formulated, applying stochastic dynamic programming, based on the following hypotheses: • The driver can only have a maximum of one accident per year, • An accident has random costs Y that depend on the severity of the claim, • In the event of an accident, the driver can notify the insurance company, in which case the premium will increase, and may not communicate, in this specific case to obtain a bonus on the premium. The main results of this model are that, depending on whether the accident costs, during the term of the contract are comparable with the premiums to be paid, the driver can bear the accident costs himself; if the costs are higher than the premium payable, then refer the accidents to the insurance company. On the other hand, it poses the problem of the need for the scale of premiums to be adjusted to the costs of the accident. Finally, it is recommended to continue this work in some directions, which it was not possible to address in this work, but which make the model more realistic, for example, it would be interesting to take into account that a driver may have more than one during the year. accident, as well as verifying the dependence of the model in relation to some random factors such as the driver's prudence, his speed of assessment and reaction to certain situations, etc... (TRADUÇÃO NOSSA)