Academic journal article Journal of Risk and Insurance

Optimal Prevention for Multiple Risks

Academic journal article Journal of Risk and Insurance

Optimal Prevention for Multiple Risks

Article excerpt

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 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. (1) The 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 prevention 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 presence of other risks. (2) These 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 international organizations over the past years. (3) We find that raising exogenously the level of protection for one risk induces a negative impact on the prevention expenditures for another unregulated risk.

To carry out our analysis, we draw on recent works that model prevention activities in a two-period expected utility framework. The idea behind this approach stems from the fact that the decision to engage in prevention activities precedes its effect on the risk, whereas the one-period model implicitly assumes that the decision to engage in prevention and its effect on the risk are simultaneous. …

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