Modelling insurance market under solvency capital requirement

Abstract

Since 2016 the operation of insurance companies in the European Union is regulated by the Solvency II directive. According to the EU directive the capital requirement should be calculated as a 99.5% of Value at Risk. In this study, we examine the impact of this capital requirement constraint on equilibrium premiums and profits. We discuss the case of the oligopoly insurance market using Bertrand's model, assuming profit maximizing insurance companies, with the same level of capital facing Value at Risk constraints. The equilibrium premium can be higher than the net premium, and the companies may achieve positive expected profit. Under certain parameters, the monopoly market or on oligopoly with a few companies with higher capital can ensure lower premium.