Insurance pricing using H∞-control

•We model an insurance company using the tools of H(infinity) control theory.•We deal with insurance pricing considering delay, randomness and uncertainty.•We obtain the optimal stabilization factor of the system using H control theory.•We calculate the values of the stabilization factor under different scenarios.

The paper considers a typical insurance system “suffering” from the three standard “curses”: (a) the stochastic nature of claims, (b) the inherent delays in claims settlement and reserving process and (c) the uncertainty concept that endows many of its parameters and especially the investment process. We construct a general multidimensional model for pricing simultaneously one, two or more different insurance products. The responsible decision maker uses the incomplete information of claims and aims to balance the system by the means of a feedback mechanism. The robust stabilization controller of the system is obtained by the means of H∞-control using typical linear matrix inequalities. Finally, a numerical application is fully investigated providing further insight into the practical problem of pricing assuming the simplest case of a portfolio with a single product.