Risk-Taking Behaviour With Expected Utility and Limited Liability: Applications to the Regulation of Financial Intermediaries

We examine the optimal risk-taking behaviour of a risk-averse individual under the assumption of a guaranteed floor for wealth (limited liability). We show that the existence of limited liability raises the optimal exposure to risk. Also, there is a positive lower bound to initial wealth (equity) under which it is optimal to accept the maximum allowed risk (''betting for ressurection''). An exogenous increase in equity does not necessarily reduces optimal exposure to risk, except if absolute risk aversion is non- decreasing. In particular, we show that increasing equity capital would increase the probability of failure if relative risk aversion is decreasing. Applications are for the regulation of the banking and insurance systems with incomplete markets and asymmetric information.