Financial/Actuarial Mathematics Seminar

When explaining insurance pricing techniques, the main motivation to explain segmentation (and the use of covariate to offer an "adapted" premium) is based on competition : if a competitor use a more detailed segmentation, our company will keep "bad" risks at an underpriced level (we were expecting to pool those risks with "good" ones, and to use the sharing - mutualization - principle). Based on that explanation, actuaries have a strong motivation to use GLMs (or more advanced predictive technique) to estimate the pure premium, the expected value of future losses. But then competition is usually forgotten by actuaries, and model choice is only based on statistical techniques, assuming that every one will remain in our portfolio. We will see mathematical problems arising when trying to model competition in an insurance market, and illustrate what might happen with "games" we have launched over the past two years. In those games, players were given a training dataset (motor insurance), and they were supposed to act as an insurance company by offering premiums on another dataset. After collecting premiums, we did mimic an insurance market by matching insured and insurer. As observed in those game, if competition deteriorates the market loss ratio, it can have very different implication on individual results. An several standard actuarial assumptions can be discussed from results obtained in those games. Speaker(s): Arthur Charpentier (Universite Rennes)