A Value at Risk Approach to Background Risk

This paper studies the effects of an uninsurable background risk (BR) on the demand for insurance (proportional and with deductible). We study both the case of BR uncorrelated with the insurable one and the perfectly correlated one, in a Gaussian world. In order to perform our study, we exploit the new risk measure known as Value at Risk (VaR) and consider insurance contracts which are Mean-VaR efficient. We obtain results which depend on the parameters (moments) of both risks and on the magnitude of loadings charged by the insurance company, instead of depending on the risk attitudes of the insured, such as risk aversion and prudence.