An Incentive‐Compatible Experiment on Probabilistic Insurance and Implications for an Insurer's Solvency Level

• DOI: http://doi.org/10.1111/jori.12148
• Date: 01 March 2018
• Published date: 01 March 2018

© 2016 The Journal of Risk and Insurance. Vol. 85, No. 1, 245–273 (2018).

DOI: 10.1111/jori.12148

245

ANINCENTIVE-COMPATIBLE EXPERIMENT ON

PROBABILISTIC INSURANCE AND IMPLICATIONS

FOR AN INSURER’SSOLVENCY LEVEL

Anja Zimmer

Helmut Gr€

undl

Christian D. Schade

Franca Glenzer

ABSTRACT

This article is the first to conduct an incentive-compatible experiment using

real monetary payoffs to test the hypothesis of probabilistic insurance, which

states that willingness to pay for insurance decreases sharply in the presence

of even small default probabilities as compared to a risk-free insurance

contract. In our experiment, 181 participants state their willingness to pay for

insurance contracts with different levels of default risk. We find that the

willingness to pay sharply decreases with increasing default risk. Our

results, hence, strongly support the hypothesis of probabilistic insurance.

Furthermore, we study the impact of customer reaction to default risk on an

insurer’s optimal solvency level using our experimentally obtained data on

insurance demand. We show that an insurer should choose to be default-free

rather than having even a very small default probability. This risk strategy is

also optimal when assuming substantial transaction costs for risk manage-

ment activities undertaken to achieve the maximum solvency level.

INTRODUCTION

After the financial crisis of 2008, financial services customers became highly

concerned about the safety of financial products. The default risk inherent in such

contracts has become a driving factor of purchase decisions, a situation highlighted by

Anja Zimmer and Christian D. Schade are at Humboldt-Universit€

at zu Berlin, School of

Business and Economics, Spandauerstr. 1, 10178 Berlin, Germany. Helmut Gr€

undl and Franca

Glenzer are at Goethe-Universit€

at Frankfurt am Main, Faculty of Economics and Business

Administration, Theodor-W.-Adorno-Platz 3, 60629 Frankfurt am Main, Germany. Helmut

Gr€

undl can be contacted via e-mail: gruendl@finance.uni-frankfurt.de. The authors would like

to thank the anonymous referees and the editor of the Journal of Risk and Insurance, Keith

Crocker, for their helpful comments that helped improve this article considerably. We also

thank the Berlin Association of Insurance Research (Verein zur F€

orderung der Versicher-

ungswissenschaft in Berlin) for its financial support.

246 THE JOURNAL OF RISK AND INSURANCE

the emergence of financial strength ratings for financial services providers.

1

In fact,

there is ample empirical evidence that awareness of default risk has an influence on

consumers’ insurance purchase behavior. Experimental research by Wakker, Thaler,

and Tversky (1997), Albrecht and Maurer (2000), and Zimmer, Schade, and Gr€

undl

(2009) show that people dislike insurance contracts with default risk and that

insurance demand is very sensitive to the insurer’s level of default risk. These studies

demonstrate that people will purchase an insurance contract that has the possibility of

defaulting only if the insurance premium is substantially reduced compared to a

default-free contract. Moreover, Zimmer, Schade, and Gr€

undl (2009) find that there

are a considerable number of consumers who will refuse to buy insurance at any level

of default risk.

The very pronounced sensitivity of individuals’ maximum willingness to pay, that is,

the insurance premium that makes individuals indifferent between purchasing

insurance and not purchasing insurance, that has been elicited in experiments cannot

be plausibly explained by expected utility theory. Instead, Wakker, Thaler, and

Tversky (1997) propose cumulative prospect theory, put forward by Tversky and

Kahneman (1992), to explain this drop in willingness to pay caused by only small

increments in the default probability. They coined the term “probabilistic insurance”

for insurance contracts that have a nonzero probability of default. While existing

experimental evidence and survey data support their theory, a rigorous incentive-

compatible test of probabilistic insurance is still missing in the literature. This gap

motivates our first research question of whether the hypothesis of probabilistic

insurance is supported by experimental evidence in an experimental setting suited to

incentivize truthful preference revelation and allowing for the implementation of

high financial stakes. To this end, we employ features of the experimental designs by

Bolle (1990) and Schade, Kunreuther, and Koellinger (2012) and modify them to

integrate a default risk. Most importantly, our experiment is carried out in the

laboratory and reveals policyholders’ willingness to pay for insurance with default

risk using large stakes of real money. Participants in this experiment stated their

maximum willingness to pay for four different insurance contracts that only differed

with respect to their default probability (0, 1, 2, and 3 percent, respectively).

We find that in the presence of default risk, individuals either refuse to purchase

insurance altogether or they demand a considerable reduction in the insurance price

compared to a default-free situation. For example, while in the case of the default-

free insurance contract, 71 percent of the participants were willing to pay at least the

actuarially fair premium, in the case of the insurance contract with a default risk of

3 percent, 50 percent of the participants were not willing to pay the actuarially fair

premium. The median willingness to pay decreases from s54 for a default-free

contract to s29 for a contract with 3 percent default probability (this compares to

actuarially fair premiums of s40 and s38.80, respectively). This strong reduction in

willingness to pay in the presence of only small default probabilities underscores how

sensitively individuals react to only small increases in default risk when purchasing

1

See AMB Credit Reports—Consumer (www.ambest.com/sales/AMBCreditReportsConsumer/

default.asp).