A Market Model of Risk Transfer and Insurance

We introduce a model of a market where risk-averse consumers pay a fee to transfer their future losses to one or more firms. The future loss of each consumer is stochastic with a unique, known mean and variance. The law of large numbers allows the firms to know with certainty the expected aggregate loss of the consumers to whom they sell. The model could describe the behavior of agents in the market for property insurance where an insurance company sells a single type of policy to a specific group of consumers based upon the expected losses of those consumers and their willingness to pay for coverage. The model demonstrates how a single firm can choose the optimal segment of the market to which they sell a policy and how that choice might change when the distribution of consumers and their risk aversion changes. The model also demonstrates how two firms might engage in a cooperative strategy and share the market. The model shows how a firm entering the market will find it more advantageous to target a segment of the market with consumers that have a lower expected loss.

Anderson, S., Palma de, A., & Thisse, J. (1992). Discrete choice theory of product differentiation. Cambridge: MIT Press.

Benoit, J., & Krishna, V. (1987). Dynamic duopoly: Prices and quantities. Review of Economic Studies, 54(1), 23-35.

Bernheim, B. D. (1984). Rationalizable Strategic Behavior. Econometrica, 52, 1007-1028.

Bertrand, J. (1883). Theorie mathematique de la richesse sociale; Recherche sur les principes mathematiques de la theorie des richesses. Journal des Savants, 499-508.

Choné, P., & Linnemer, L. (2019). The quasilinear quadratic utility model: An overview. Hal Open Science, HAL Id: hal-02318633 https://hal.archives-ouvertes.fr/hal-02318633, 2019.

Dewatripont, M. (1987). The role of indifference in sequential models of spatial competition. Economics Letters, 23, 23-328.

Dixit, A. (1980). The role of investment in entry deterrence. Economic Journal, 90(3), 95-106.

Donnenfeld, S., & Weber, S. (1992). Vertical product differentiation with entry. International Journal of Industrial Organization, 10(9), 449-472.

Eaton, B., & Ware, R. (1987). Theory of market structure with sequential entry. The Rand Journal of Economics, 18, 1-16, Spring.

Harris, C. (1985). Existence and characterization of perfect equilibrium in games of perfect information. Econometrica, 53(5), 613-616.

Hay, D. (1976). Sequential entry and entry-deterring strategies in spatial competition. Oxford Economic Papers, 2(7), 240-257.

Lane, W. (1980). Product differentiation in a market with sequential entry. Bell Journal of Economics, 11, 237-260, spring.

Lehmann-Grube, U. (1997). Strategic choice of quality when quality is costly: The persistence of the high-quality advantage. RAND Journal of Economics, 28, 372-384.

Leland, H. (1977). Quality choice and competition. American Economic Review, 67(3), 127-137.

Mclean, R., & Riordan, M. (1989). Industry structure with sequential technological choice. Journal of Economic Theory, 47(2), 1-21.

Mussa, M., & Sherwin, R. (1978). Monopoly and product quality. Journal of Economic Theory, 18(8), 301-317.

Prescott, E., & Visscher, M. (1977). Sequential location among firms with foresight. Bell Journal of Economics, 8, 378-393, Autumn.

Schwartz, M., & Baumann, M. (1988). Entry-deterrence externalities and relative firm size. International Journal of Industrial Organization, 6(6), 181-197.

Schwartz, M., & Thompson, E. (1986). Divisionalization and entry deterrence. Quarterly Journal of Economics, 101(5), 307-321.

Shaked, A., & Sutton, J. (1982). Relaxing price competition through product differentiation. Review of Economic Studies, 49(1), 3-14.

Sutton, J. (1997). One smart agent. RAND Journal of Economics, 28, 605-628, winter.

Tirole, J. (1988). The Theory of Industrial Organization. Cambridge: MIT Press.

Vives, X. (1988). Sequential entry, industry structure and welfare. European Economic Review, 32(10), 1671-1687.

Wauthy, X. (1996). Quality choice in models of vertical differentiation. The Journal of Industrial Economics, 44, 345-353.