Optimal Prevention for Multiple Risks

• Published date: 01 September 2017
• Author: Richard Peter,Christophe Courbage,Henri Loubergé
• DOI: http://doi.org/10.1111/jori.12105
• Date: 01 September 2017

©2015 The Journal of Risk and Insurance. Vol.84, No. 3, 899–922 (2017).

DOI: 10.1111/jori.12105

Optimal Prevention for Multiple Risks

Christophe Courbage

Henri Louberg´

e

Richard Peter

Abstract

This article analyzes optimal prevention in a situation of multiple, possi-

bly correlated risks. We focus on probability reduction (self-protection) so

that correlation becomes endogenous. If prevention concerns only one risk,

introducing a second exogenous risk increases the level of prevention expen-

ditures, even if correlation is negative. If prevention expenditures may be

invested for both risks, a substitution effect arises. Under nonincreasing re-

turns on self-protection, we find that increased dependence increases aggre-

gate prevention expenditures, but not necessarily prevention expenditures

for each risk due to differences in prevention efficiency. Similar results are

found when considering changes in the severity of losses. Consequently,the

comparative statics emphasize global effects versus allocation effects.Our re-

sults have strong policy implications, considering the numerous mandatory

safety measures introduced by governments over the past years.

Introduction

Individuals and firms face multiple risks. Some of them are independent but others are

dependent. For example, the risk of damage to the roof is often associated to the risk of

flooding; the risk of releasing hazardous waste in the environment may be associated

to the risk of suffering virus attacks on the information system; the risk of workers’

injuries is known to be negatively correlated with the credit risk of consumers due to

Christophe Courbage is at The Geneva Association and the Haute Ecole de Gestion de Genève,

University of Applied Sciences Western Switzerland (HES-SO). Henri Louberg´

e is at the Uni-

versity of Geneva and Swiss Finance Institute. Richard Peter is at the Department of Finance,

Henry B. Tippie College of Business, University of Iowa. Peter can be contacted via e-mail:

richard-peter@uiowa.edu. Wewould like to thank participants in the 41st Seminar of the Euro-

pean Group of Risk and Insurance Economists in St. Gallen and particularly Harris Schlesinger;

participants in the American Risk and Insurance Association Annual Meeting 2014 in Seattle

and particularly Carole Bernard; participants in the 13th Louis-Andr´

eG

´

erard-Varet Meeting

in Public Economics at the University of Aix-Marseille and particularly Mukul Tyagi; and

seminar participants at the Economics Research Seminar, University of Geneva, the Journ´

ees

Internationales du Risque in Niort, the Economics and Finance Visiting Speaker Series at the

University of Guelph and the RMI Speaker Series at St. John’s University in New York for

valuable comments and discussions.

899

900 The Journal of Risk and Insurance

their common link to the business cycle. Some of the risks may be avoided by taking

radical measures, for example, giving up the pleasure of skiing to avoid the risk of

a ski accident, or giving up the development of a new product to avoid potential

product liability suits. When the risks cannot, or should not, be avoided they may be

managed by prevention and loss reduction measures or transferred to an insurer. The

article focuses on prevention as a risk management tool.

Prevention is an ex ante activity that reduces the probability of a loss.1The economic

analysis of prevention started with the seminal work of Ehrlich and Becker (1972) and

has led since then to a flourishing literature (Courbage, Rey, and Treich, 2013). But,

the canonical model, developed along several dimensions, assumes that the decision

maker (DM) faces only one risk to be mitigated using prevention measures, such as

investing in fire-proof materials to reduce the probability of fire, or investing in locks

and alarms to reduce the probability of burglary. Given that firms and individuals face

multiple risks, the question we ask in this article is how the decision to prevent one

risk interacts with the decision to prevent other risks. More particularly, we wonder

how the characteristics of the multiple risks and the efficiency of alternative preven-

tion instruments influence the decision to invest in a specific portfolio of prevention

measures. For instance, if we consider two risks and if the dependence between the

two risks increases, will the DM increase his total investment and the level of both

prevention activities? How will he alter the composition of his portfolio of prevention

measures? Our analysis can also help to predict the effect of imposing mandatory

prevention expenditures for one risk on the decision to prevent other risks.

While the literature on economic decisions in a multiple-risk setting is quite abundant,

only a few articles have recently addressed the study of self-protection in the pres-

ence of other risks.2These articles look at either the relation between self-protection

and risk aversion in the presence of an independent zero-mean background risk

(Dachraoui et al., 2004) or the impact of an independent zero-mean background

risk on self-protection activities in a one-period model (Lee, 2012) or a two-period

model (Eeckhoudt, Huang, and Tzeng, 2012; Courbage and Rey, 2012; Wang and

Li, forthcoming). Our article differs markedly from the above literature in three

ways. First, we allow for nonzero correlation between the different sources of risk.

This is motivated, among other things, by recent empirical evidence (Sun and Frees,

2013). Second, we also consider the decision to prevent both risks simultaneously,

and not merely the influence of the second risk on optimal prevention for the first

risk. Third, we derive policy implications from our analysis by investigating the

impact of exogenous changes in the level of prevention for one risk on the optimal

self-protection investment for the other risk. This allows us to assess the side effects

of the numerous mandatory safety measures introduced by governments and

1Following Ehrlich and Becker’s (1972) terminology, this activity is also referred to as self-

protection. Throughout the article, we use both terms synonymously.

2Note, however, the contributions of Briys, Schlesinger, and von der Schulenburg (1991) and

Schlesinger (1992) considering the reliability of prevention expenses. There is only one risk

in the endowment, but the possible failure of prevention measures introduces an additional

(multiplicative) risk.