Academic journal article Journal of Risk and Insurance

Insurance Demand under Prospect Theory: A Graphical Analysis

Academic journal article Journal of Risk and Insurance

Insurance Demand under Prospect Theory: A Graphical Analysis

Article excerpt

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; Dreze, 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).

The standard theory of decision making under risk, expected utility (EU) theory, is not able to explain these phenomena. Under EU, a subject will buy full insurance if and only if premiums are fair, that is, equal expected losses. This excludes not taking up subsidized flood insurance or buying highly loaded cellular-phone insurance. Also fitting the demand for low deductibles to EU leads to implausible high degrees of risk aversion (Sydnor, 2010). While EU is primarily a normative theory of decision making under risk, descriptive alternatives to EU like prospect theory (PT) (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992) have not yet been successfully employed to organize the evidence. Although PT is currently one of the most prominent descriptive theories of decision making under risk, there exist only very few studies applying PT to insurance demand. One reason for this may be the fact that it is not obvious what the right reference point for such an analysis should be. Usually the status quo is taken as reference point under PT. Accordingly, Wakker et al. (1997) and Sydnor (2010) take initial wealth--that is, the wealth if no loss occurs--as reference point. The main problem, as argued by Sydnor, is the fact that the decision to take up insurance is then determined entirely in the loss domain, where subjects are according to PT in general risk seeking. With overweighting of small probabilities, risk aversion for improbable losses can occur under PT, but also in this case the high demand for insuring modest risks cannot be explained.

In the present article, we argue that it is questionable whether initial wealth is the right choice of the reference point for analyzing insurance problems with PT. Consider a simple insurance problem where the subject has initial wealth w but in one state of the world a loss L might occur such that final wealth equals w - L in this state. Wakker et al. (1997) and Sydnor (2010) take w as reference point. …

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