Equitable solvent controls in a multi-period game model of risk

In insurance two major types of cycles are known: (a) regular many years long up- and down-swings referred to as underwriting cycles and (b) irregular short-range fluctuations. The key rationale of the underwriting cycles is migration of insureds triggered by the insurers' price competition while the short-range fluctuations are due to unpredictable fluctuations in economic surroundings. The competition-originated cycles were modeled in the framework of a Lundberg's-type multi-period model of risk in Malinovskii (2010, submitted for publication). Short-range fluctuations were modeled under diverse nature scenarios in the framework of (i) diffusion (see Malinovskii, 2007, 2009) and (ii) Lundberg's-type multi-period model (see Malinovskii, 2008a). In this paper the results of Malinovskii (2009) are extended on the Lundberg's-type multi-period model.

► We model the insurance process of a company over an n-year horizon. ► We introduce a multi-period Lundberg's-type model of risk. ► We construct strategies meeting fluctuations in economic surroundings. ► We examine equity and solvency of the control strategies.