Success and Failure of the Financial Regulation on a Surplus-Driven Financial Company

This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a quantile-based constraint (a Value-at-Risk or an Average Value-at-Risk constraint), or a shortfall-based constraint (an expected shortfall or an expected discounted shortfall constraint). We obtain closed-form solutions to the optimal wealth for the non-concave utility maximization problem under constraints. We find that the quantile- and shortfall-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits typically cannot be fully protected under either type of regulation.