Optimal insurance with background risk: An analysis of general dependence structures

Optimal Incentive-Compatible Insurance With Background Risk

“…More precisely, this part of risk is often not ceded for the former case, especially when (4.1) is satisfied, but it is transferred to some degree in the latter case. These two propositions show that the optimal insurance contract can be in the form of a combination of layer insurance for middle risk and partial insurance for tail risk, which is quite different from previous studies except Chi and Wei (2020). More precisely, in the absence of background risk, layer insurance and partial insurance above a deductible are often shown to be optimal, especially under some risk measure; see, for example, Raviv (1979), Tan (2011), Chi (2012).…”

“…We leave this to future research. It is necessary to point out that, following this work, Lu et al (2018), Chi and Wei (2018) and Chi and Wei (2020) have made contributions to this problem within the expected utility framework. must exist a κ * such that E[I κ * (X )] = E[I(X )].…”

“…This can be achieved via an optimisation problem such as minimising an appropriate risk measure on T I (X ;Y ) or maximising the expected utility of the insured's final wealth. When analysing the optimal insurance design under the expected utility framework, besides the difficulty in eliciting the utility function from the insured, the solution is seldom derived explicitly except for some special types of dependence between background risk and the insurable risk (see Chi and Wei, 2020). Motivated by the popularity of the mean-variance optimisation criterion in finance and insurance, this work studies the optimal insurance design by also assuming that the insured has a general mean-variance preference.…”

Risk Sharing with Multiple Indemnity Environments

“…For the monetary risk measure, the technical difficulty of the problem to find Pareto optimal contracts with multiple indemnity environments is to include mutually exclusive background risk into the risk sharing approach. Also, a more realistic situation would be that the seller is endowed with background risk that is due to potential other business lines (see, e.g., Chi & Wei, 2020;Dana & Scarsini, 2007 ). We leave these two problems open for further research.…”

“…For instance, Mahul & Wright (2003) show that indemnity functions depend not only on the underlying loss, but also on other factors such as the individual yield and/or price for crop revenues. Moreover, Dana & Scarsini (2007) and Chi & Wei (2020) show that optimal indemnities can depend on exogenous background risk. In all three papers, it is thus shown that exogenous events may influence the optimality of indemnity contracts.…”