Description: For the purposes of risk management and stress testing, we characterize a spectrum of plausible extreme events, that we dub Grey Swans, by introducing a probabilistic method involving the concentration of measure phenomenon. As a result, stress tests can be triaged according to severity, probability and, now, information-based plausibility.

Description: For the purposes of risk management and stress testing, we characterize a spectrum of plausible extreme events, that we dub Grey Swans, by introducing a probabilistic method involving the concentration of measure phenomenon. As a result, stress tests can be triaged according to severity, probability and, now, information-based plausibility.

Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.