Roy's safety-first portfolio principle in financial risk management of disastrous events

Roy pioneers the concept and practice of risk management of disastrous events via his safety-first principle for portfolio selection. More specifically, his safety-first principle advocates anoptimal portfolio strategy generated from minimizing the disaster probability, while subjectto the budget constraint and the mean constraint that the expected final wealth is not less thana preselected disaster level. This article studies the dynamic safety-first principle in continu-ous time and its application in asset and liability management. We reveal that the distortionresulting from dropping the mean constraint, as a common practice to approximate the orig-inal Roy’s setting, either leads to a trivial case or changes the problem nature completelyto a target-reaching problem, which produces a highly leveraged trading strategy. Recogniz-ing the ill-posed nature of the corresponding Lagrangian method when retaining the meanconstraint, we invoke a wisdom observed from a limited funding-level regulation of pen-sion funds and modify the original safety-first formulation accordingly by imposing an upperbound on the funding level. This model revision enables us to solve completely the safety-first asset-liability problem by a martingale approach and to derive an optimal policy thatfollows faithfully the spirit of the safety-first principle and demonstrates a prominent natureof fighting for the best and preventing disaster from happening. Copyright © 2012 Society for Risk Analysis.