Question: I'm currently delving into the realm of Markov models to understand how they can be applied to determine the cost of car insurance. Thus far, I've come across the bonus-malus system and hidden Markov chains. However, I'm curious to learn about other Markov models that could be relevant in this context. Could someone shed light on additional models or elaborate on how these models are utilized in determining car insurance costs?
Background: In my exploration of car insurance cost determination, I've encountered the bonus-malus system, which adjusts premiums based on the insured's claim history, and hidden Markov chains, which model the underlying states affecting claim occurrence. While these are insightful, I'm keen to broaden my understanding by discovering other Markov models applicable to this domain.
Criteria for Response: Short explanation of additional Markov models relevant to determining car insurance costs. Insights into how these models are applied in the insurance industry.
Thank you in advance for your expertise and insights
In car insurance, a portfolio might be divided into classes depending on their claim experience. For each class an individual premium is calculated by methods such as marginal sums, generalized linear models, etc. In my experience, Markov models are not used solely for premium calculation in car insurance. However, as you already indicated, the dynamic adjustment of a driver‘s premium (according to the classes) might be modeled using a Markov process. In practice, the premium is often based upon more detailed information than just the number of claims in the previous period.
In actuarial science, Markov models are especially used in life insurance to model states of an individual over time (e.g. healthy, disabled, dead). Such a model could be an inhomogeneous Markov-Process. Discrete models in industry are provided, e.g., as mortality-tables.
A good book I can recommend is Asmussen, Steffensen: Risk an Insurance.