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A dynamic model of an insurer: loss shocks, capacity constraints and underwriting cycles


Purpose
This paper aims to revisit the assumption of the cyclicality of the property-liability insurance market and identify a scenario in which the so-called underwriting cycles are unpredictable, according to a dynamic cash flow model which generates non-cyclical output dynamics.


Design/methodology/approach
This paper is on the intersection of real business cycle models and financial cycles. The authors construct a dynamic model of an insurer’s cash flows with stochastic loss shocks and capacity constraints, in which loss shocks have a dual impact on both underwriting profits and access to external capital. They simulate the insurer’s optimal output responses to loss shocks, including output movements in underwriting coverage and external capital, to explore the source of unpredictable underwriting cycles through linear quadratic approximation in the model economy.


Findings
The authors find that the effect of loss shocks on the insurer’s cash flows could spread out and amplify over time because of the dynamic interaction between its underwriting capability and ability to raise external capital. This dynamic interaction can generate a non-cyclical pattern of changes in underwriting coverage and access to external capital in the benchmark economy. Applied to different experimental economies, the simulation results reveal that the determinants of the level of output fluctuations include the size of loss shocks, the sensitivity of capital market to loss shocks and the tightness of capital market.


Originality/value
To the best of the authors’ knowledge, there has been no attempt to study insurance output cyclicality with a dynamic cash flow model based upon the real business cycle literature, in which the dynamic interaction between underwriting and access to external capital because of loss shocks has an amplifying effect on output markets. This paper contributes to the current body of research by being able to simulate and show the insurance output dynamics resulting from the amplifying effect under capacity constraints.
