Risk & Insurance

In a series of papers jointly with staff members of the International Institute of Applied Systems Analysis (IIASA, Austria) Amendola A., Ermoliev Y.M., MacDonald G., Ermolieva T.Y.) we develop a number of models for insurance and mitigation against rare large claims caused by catastrophic events (earthquakes, hurricanes, storms, floods, droughts, fires, financial crises and etc.). These are portfolio (also welfare, equilibrium, risk process) type models which have a form of stochastic (two-stage, dynamic) programming problems, describing trade-off between expected profit and risk of bankruptcy of an insurance company. Decision variables are fractions of insured damages. The essential part of the approach is a Monte Carlo simulation of catastrophes and subsequent dependent claims. Mathematical results (my main contribution) include reduction of chance constrained stochastic optimization problem to optimization of penalized expected profit, the development and investigation of an adaptive Monte Carlo optimization method, estimation of the probability of ruin for the case of rare dependent claims.

In Ermoliev et al. (1998, 2000) it was shown that optimal values of a chance constrained problem and a simple recourse one become close if a reliability level tends to one and recourse (penalty) prices tend to infinity.

Selected references

Ermoliev Y.M., Ermolieva T.Y., MacDonald G. and Norkin V.I. (2000). Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks, Annals of Operations Research 99, 2000, 207-225.(see also IIASA Interim Report IR-98-056, Abstract).

Amendola A., Ermoliev Y.M., Ermolieva T.Y., MacDonald G.J. and Norkin V.I. (2000). A system approach to management of catastrophic risks (Abstract), European J. of Operational Research, 2000, V.122, P.452-460.

Ermoliev Y.M., Ermolieva T.Y., MacDonald G.J. and Norkin V.I. (2000). Insurability of catastrophic risks: the stochastic optimization model (Abstract), Optimization, 2000, Vol. 47, 251-265.

Ermoliev Y.M., Ermolieva T.Y., MacDonald G. and Norkin V.I. (2000). Problems of catastrophic risks insurance, Kibernetika i sistemnyi analiz (in Russian, English translation in Cybernetics and Systems Analysis, 2001, Vol. 37, Issue 2, pp. 220-234), 2001, N 2, 99-110.

Norkin V.I. (1999). On modeling spatial, temporal and magnitude aspects in insuring cataclysmic events, Proceedings of the Second International School on Actuarial and Finantial Mathematics, Kyiv, Ukraine, 8-12 June, 1999, Theory of Stochastic Processes(Kiev), 1999, №1-2, 98-110.

Ermoliev Y.M. and Norkin V.I. (2003). Risk and Extended Expected Utility Functions: Optimization Approaches, Interim Report IR-03-033, Int. Inst. for Appl. Syst. Anal., 2003, 23p.

Norkin V.I. On self-insurance of an investor under repeating catastrophic risks // Kibernetika i sistemnyi analiz , 2007, N 2 (in Russian, English translation will appear in Cybernetics and systems analysis).

Norkin V.I. On measuring and profiling catastrophic risks // Cybernetics and systems analysis. – Vol. 42 (2006). – No.6. – P. 839-850. (Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 80–94, 2006).