Pricing in a Competitive Insurance Market Driven by Fractional Noise

Motivated by the empirical evidence of the long-range dependency found within the Greek motor insurance market, we formulate a particular stochastic pricing model in a continuous framework. We assume the structure of a competitive insurance market where the business volume of each company is directly related to the existing relativity between the company’s premium and the market’s average premium. Using a simple demand function and modeling the movements of the market via a fractional Brownian motion, we derive the optimal premium control strategy. Finally, we support the importance of the specific approach by a short application. It is shown that the optimal premium strategy is considerably different under the absence or existence of the long-range dependency.