A theory of risk, return and solvency

In recent years, state regulators and state and federal lawmakers in the United States have become increasingly concerned with issues involving both the price and solvency regulation of insurers. In this article, we develop a risk-theoretic framework for studying both rate of return and solvency issues. Employing a certain class of diffusion processes to model insurer net worth, we use the expected discounted cost of insolvency (EDCI), a generalization of the probability of ruin, in constructing the regulator's objective function. This objective function is then used to solve for the optimal rate of return and the optimal loss-to-net worth ratio.