Continuous Monitoring: Look before you Leap

We study a limited liability non-life insurance company, and present a valuation model of the insurance customers' financial loss in the case where the insurance company defaults. In the case of continuous monitoring, i.e., where the market values of the company's assets and liabilities are continuously observable, and where the market values of assets and liabilities follow continuous processes, the insurance customers will never suffer a loss because regulators can stop the insurance company's business at the instant the market value of its assets equal the market value of its liabilities. When jumps are included in the claims process, the insurance customers may face a loss, and the protection offered by the guarantee fund thus have a strictly positive market value. We suggest that the ability to continuously monitor the equity value of a company as a new explanation for why jump processes may be important in the study of credit risk.