Optimal insurance risk allocation with steepest ascent and genetic algorithms

Purpose – Enhanced risk management through the application of mathematical optimization is the next competitive-advantage frontier for the primary-insurance industry. The widespread adoption of catastrophe models for risk management provides the opportunity to exploit mathematical optimization techniques to achieve superior financial results over traditional methods of risk allocation. The purpose of this paper is to conduct a numerical experiment to evaluate the relative performances of the steepest-ascent method and genetic algorithm in the solution of an optimal risk-allocation problem in primary-insurance portfolio management. Design/methodology/approach – The performance of two well-established optimization methods – steepest ascent and genetic algorithm – are evaluated by applying them to solve the problem of minimizing the catastrophe risk of a US book of policies while concurrently maintaining a minimum level of return. Findings – The steepest-ascent method was found to be functionally dependent on, but not overly sensitive to, choice of initial starting policy. The genetic algorithm produced a superior solution to the steepest-ascent method at the cost of increased computation time. Originality/value – The results provide practical guidelines for algorithm selection and implementation for the reader interested in constructing an optimal insurance portfolio from a set of available policies.