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 [1994], Grosen and Jørgensen [2002] and Chen and Suchanecki [2007]. We
show that if the insurance company follows a risk management strategy, it can significantly
change the risk exposure of the company, and that it should thus be taken into account
by the regulators. We first study how the regulator establishes regulation intervention
levels in order to control for instance the default probability of the insurance company (under
the real world probability measure). This part of the analysis is based on a constant
volatility and there exists a one-to-one relation between the optimal regulation level and
the volatility. Given that the insurance company is informed of the 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 the limits of prior
literature and believe that the value of the risk management of the company should be
included in the risk exposure estimation and the market value of liabilities as well.