Insurance risk exchange in the presence of background risk and private information

Purpose – The purpose of this study is to introduce an insurance risk‐exchange model in the presence of background risk and private information and which solves the optimal insurance and investment decisions simultaneously. Design/methodology/approach – The model undertakes a continuous‐time two‐agent framework in which the decisions depend on who can determine the insurance quantity as well as the agents' risk attitudes. The decisions are solved by using dynamic‐programming techniques. Findings – The results show that the insured may purchase full insurance even if the insurance price is actuarially unfair and the insurance risk and investment risk are uncorrelated. Further, the demand for insurance may be affected by background risk even if the two risks are uncorrelated. If Pareto optimality is impeded by private information, the paper shows that the deadweight loss can be mitigated by forming a hedging demand with respect to the parameter risk. Originality/value – This study is not only an extension of the existing continuous‐time insurance demand model, but also may be considered a model of “enterprise risk management” for institutional agents.