# Insurance market equilibrium: a multi-period dynamic solution

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## Abstract

Purpose – This article aims to apply a multi-period model of insurance market equilibrium to solve for the insureds' optimal demand for insurance, as well as insurers' optimal supply. Design/methodology/approach – Most approaches to competitive equilibrium in the insurance market involve the construction of demand and supply curves based on maximizing the insureds' and insurers' expected utility for a single time period. However, it is important to recongnize that, for a given utility function, the demand (supply) decisions of insureds (insurers) in a single-period model may differ substantially from those under a multi-period formulation. In this article, first, separate multi-period models of demand and supply are constructed, and then a dynamic solution for equilibrium price and quantity is provided. Findings – Although a single-period model generally requires the assumption of an exact loss distribution to compute expected utilities, the multi-period model requires only the expected loss and its associated stochastic process (in this case, a Brownian motion). One implication of this approach is that it may explain phenomena of market prices failing to achieve Pareto optimality for a single period. Originality/value – This approach may be used to generate new hypotheses related to the underwriting cycle. Specifically, the insureds' demand and insurers' supply decisions may both be based on expected discounted future cash flows. The non-trivial multi-period equilibrium insurance price may provide additional insights into the volatility of insurance market prices.

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