On the regulator-insurer interaction in a structural model

In this paper, we provide a new insight to the previous work of Briys and de Varenne [E. Briys, F. de Varenne, Life insurance in a contingent claim framework: Pricing and regulatory implications, Geneva Papers on Risk and Insurance Theory 19 (1) (1994) 53-72], Grosen and Jørgensen [A. Grosen, P.L. Jørgensen, Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework, Journal of Risk and Insurance 69 (1) (2002) 63-91] and Chen and Suchanecki [A. Chen, M. Suchanecki, Default risk, bankruptcy procedures and the market value of life insurance liabilities, Insurance: Mathematics and Economics 40 (2007) 231-255]. We show that the particular risk management strategy followed by the insurance company can significantly change the risk exposure of the company, and that it should thus be taken into account by regulators. We first study how the regulator establishes regulation intervention levels in order to control for instance the default probability of the insurance company. This part of the analysis is based on a constant volatility. Given that the insurance company is informed of regulatory rules, we study how results can be significantly different when the insurance company follows a risk management strategy with non-constant volatilities. We thus highlight some limits of the prior literature and believe that the risk management strategy of the company should be taken into account in the estimation of the risk exposure as well as in that of the market value of liabilities.