INSURANCE DEMAND UNDER PROSPECT THEORY: A GRAPHICAL ANALYSIS

• Date: 01 January 2016
• Author: Ulrich Schmidt
• DOI: http://doi.org/10.1111/jori.12098
• Published date: 01 January 2016

INSURANCE DEMAND UNDER PROSPECT THEORY:

AG

RAPHICAL ANALYSIS

Ulrich Schmidt

ABSTRACT

This article analyzes insurance demand under prospect theory in a simple

model with two states of the world and fair insurance contracts. We argue

that two different reference points are reasonable in this framework, state-

dependent initial wealth or final wealth after buying full insurance.

Applying the value function of Tversky and Kahneman (1992), we find

that for both reference points subjects will either demand full insurance or no

insurance at all. Moreover, this decision depends on the probability of the

loss: the higher the probability of the loss, the higher is the propensity to take

up insurance. This result can explain empirical evidence that has shown that

people are unwilling to insure rare losses at subsidized premiums and at the

same time take up insurance for moderate risks at highly loaded premiums.

INTRODUCTION

A major puzzle in insurance economics is the fact that people underinsure low-

probability events with high losses and overinsure moderate risks. It is well

documented that many people do not take up disaster insurance even though

premiums for such insurance contracts are often subsidized (Kunreuther et al., 1978;

Kunreuther and Pauly, 2004). A very prominent example for this type of behavior is

flood insurance in the United States. At the same time, for modest risk people do often

buy insurance with premiums exceeding expected losses substantially (Pashigian

et al., 1966; Dr

eze, 1981; Cutler and Zeckhauser, 2004; Kunreuther and Pauly, 2006;

Sydnor, 2010). Examples here are demand for low deductibles and markets for

extended warranties or cellular-phone insurance. Beside the cited evidence from the

field, also several experimental studies indicate that—holding loading factor and

expected loss constant—the rate of insurance take-up increases with the probability of

the loss (Slovic et al., 1977; McClelland et al., 1993; Ganderton et al., 2000; but see also

the contrary results of Laury et al., 2009).

Ulrich Schmidt is at the Kiel Institute for the World Economy, D€

usternbrooker Weg 120, 24105

Kiel and at the Department of Economics, University of Kiel, and at the Department of

Economics and Econometrics, University of Johannesburg. He can be contacted via e-mail:

ulrich.schmidt@ifw-kiel.de. The author thanks Peter P. Wakker, Glenn W. Harrison, and two

anonymous referees for helpful comments.

©2015 The Journal of Risk and Insurance. Vol. 83, No. 1, 77–89 (2016).

DOI: 10.1111/jori.12098

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