Some insurance markets are affected by the well-known phenomenon of “underwriting cycles,” made up of a tight phase during which premiums and profits increase while capacities decline, followed by a slacker period, characterized by lower prices and replenished capacities. It is difficult to explain these cycles within the classic framework of perfect financial markets. They imply a certain degree of predictability for premiums, a correlation between insurance company ROE and claims, which appears to contradict the principle of the no-arbitrage condition.
We demonstrate that these properties can be perfectly well explained in a competitive equilibrium model with financial frictions. Our model extends the classic approach of ruin theory to a macroeconomic model where insurance premiums are endogenous and result from the balance between policy supply and demand. Companies determine their underwriting policies and stock issuance and buyback policies in a way calculated to maximize their stock share price. Insurance premiums are a deterministic function of the total market capitalization of all insurance companies.
Our results explain why insurance premiums are predictable, as well as the correlation between ROE and claims. In fact, rather than genuine cycles, premiums and capacities oscillate between two extreme values with trends changing direction once one of these two values is attained. Our model illustrates the power of the new generation of macroeconomic models with financial frictions, introduced by Brunnermeier and Sannikov (2014), which can be successfully applied to the analysis of other important questions for insurance and reinsurance markets.