Perspectives of Risk Sharing
- 1 January 2002
- journal article
- research article
- Published by Informa UK Limited in Scandinavian Actuarial Journal
- Vol. 2002 (2), 73-128
- https://doi.org/10.1080/03461230110106237
Abstract
In this paper we present an overview of the standard risk sharing model of insurance. We discuss and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums. We only touch upon the existence problem of a competitive equilibrium, primarily by presenting several examples. Risk tolerance and aggregation is the subject of one section. Risk adjustment of the probability measure is one topic, as well as the insurance version of the capital asset pricing model. The competitive paradigm may be a little demanding in practice, so we alternatively present a game theoretic view of risk sharing, where solutions end up in the core. Properly interpreted, this may give rise to a range of prices of each risk, often visualized in practice by an ask price and a bid price. The nice aspect of this is that these price ranges can be explained by "first principles", not relying on transaction costs or other frictions. We also include a short discussion of moral hazard in risk sharing between an insurer and a prospective insurance buyer. We end the paper by indicating the implications of our results for a pure stock market. In particular we find it advantageous to discuss the concepts of incomplete markets in this general setting, where it is possible to use results for closed, convex subspaces of an L 2 -space to discuss optimal risk allocation problems in incomplete financial markets.Keywords
This publication has 40 references indexed in Scilit:
- Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless assetJournal of Mathematical Economics, 1999
- The Values of Insurance Companies Under Different Uncertain PortfoliosThe Geneva Risk and Insurance Review, 1996
- Insurance and Precautionary Capital Accumulation in a Continuous-Time ModelJournal of Risk and Insurance, 1994
- Dynamic Equilibrium and the Structure of Premiums in a Reinsurance MarketThe Geneva Risk and Insurance Review, 1992
- Existence Theorems in the Capital Asset Pricing ModelEconometrica, 1991
- Uniqueness of Equilibrium in the Classical Capital Asset Pricing ModelJournal of Financial and Quantitative Analysis, 1988
- Portfolio Selection in the Mean-Variance Model: A NoteThe Journal of Finance, 1987
- Arbitrage and the Existence of Competitive EquilibriumEconometrica, 1987
- Moral Hazard and ObservabilityThe Bell Journal of Economics, 1979
- An aggregation theorem for securities marketsJournal of Financial Economics, 1974