Abstract
In this paper we analyze insurance demand when the utility function depends both upon final wealth and the level of losses or gains relative to a reference point. Besides some comparative statics results, we discuss the links with first-order risk aversion, with the Omega measure, and with a tendency to over-insure modest risks that has been been extensively documented in real insurance markets.
Highlights
In his early and deep contributions to the insurance economics literature, Borch (1960, 1962) made the assumption that the decision-maker’s utility function depends only upon his/her final wealth.This assumption was adopted for decades in the analysis of insurance choice, and a recent survey of this literature by Schlesinger (2013) confirms this observation.Borch’s assumption has been considered and developed in a number of papers, in conjunction with Yaari (1987) dual theory of choice and its implications for insurance demand.An exception to Borch’s assumptions resulted from the distinction made by Segal and Spivak (1990)between second-order and first-order risk aversion
In accordance with Davies and Satchell (2007), we examine the characteristics of πv for sufficiently small risks by taking a first-order Taylor approximation around the reference point on the left-hand side (LHS) of the above equation: LHS ≈ v(r ) − πv (r, t)v0− (r ) ≈ u(r ) − πv (r, t)(1 + λη )u0 (r )
The optimal proportion of insurance coverage αr∗ that maximizes Equation (11) is always larger than the optimal proportion of insurance coverage α∗ implied by a conventional utility function u that exhibits
Summary
In his early and deep contributions to the insurance economics literature, Borch (1960, 1962) made the assumption that the decision-maker’s utility function depends only upon his/her final wealth. In Guo’s model, preferences are consistent with a set of stochastic dominance rules for ordering risks in the presence of an exogenous target Based on these rules, we prove an extension of Arrow’s theorem of the deductible (Arrow 1974) showing that, under FORA, risk-averse decision-makers maintain a preference for concentrating insurance coverage in the states with the largest losses. A promising direction for future research is the “Third-generation prospect theory” introduced by Schmidt et al (2008) combining reference dependence, decision weights, and an uncertain reference point Based on these considerations, we believe that it may be useful to explore the implications of allowing a two-argument utility function for insurance demand, and we show here that the model of Guo et al (2016) provides a tractable framework for this analysis.
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