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Optimal reinsurance under multiple attribute decision making

Published online by Cambridge University Press:  17 November 2015

Başak Bulut Karageyik  and
David C.M. Dickson
Başak Bulut Karageyik
Affiliation:
Department of Actuarial Science, Hacettepe University, 06800 Beytepe, Ankara, Turkey
David C.M. Dickson*
Affiliation:
Department of Economics, Centre for Actuarial Studies, University of Melbourne, VIC 3010, Australia
*
*Correspondence to: David C.M. Dickson, Department of Economics, Centre for Actuarial Studies, University of Melbourne, VIC 3010, Australia. Tel: +61 3 8344 4727; Fax: +61 3 8344 6899; E-mail: dcmd@unimelb.edu.au
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Abstract

We apply methods from multiple attribute decision making (MADM) to the problem of selecting an optimal reinsurance level. In particular, we apply the Technique for Order of Preference by Similarity to Ideal Solution method with Mahalanobis distance. We consider the classical risk model under a reinsurance arrangement – either excess of loss or proportional – and we consider scenarios that have the same finite time ruin probability. For each of these scenarios we calculate three quantities: released capital, expected profit and expected utility of resulting wealth. Using these inputs, we apply MADM to find optimal retention levels. We compare and contrast our findings with those when decisions are based on a single attribute.

Keywords

ReinsuranceRuin probabilityTranslated gamma processMultiple attribute decision makingTOPSIS
Type
Papers
Information
Annals of Actuarial Science , Volume 10 , Issue 1 , March 2016 , pp. 65 - 86
Copyright
© Institute and Faculty of Actuaries 2015 

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References

Antucheviciene, J., Zavadskas, E.K. & Zakarevivius, A. (2010). Multiple criteria construction management decisions considering relations between criteria. Technological and Economic Development of Economy, 16, 109–125.Google Scholar
Borch, K. (1990). Economics of Insurance. North-Holland, Amsterdam.Google Scholar
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. & Nesbitt, C.J. (1997). Actuarial Mathematics, 2nd edition. Society of Actuaries, Itasca, IL.Google Scholar
Centeno, L. (1986). Measuring the effects of reinsurance by the adjustment coefficient. Insurance: Mathematics & Economics, 5, 169–182.Google Scholar
Chi, Y. & Tan, K.S. (2011). Optimal reinsurance under VaR and CVaR risk measures: a simplified approach. ASTIN Bulletin, 41, 487–509.Google Scholar
Dickson, D.C.M. (2005). Insurance Risk and Ruin. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1993). Gamma processes and finite time survival probabilities. ASTIN Bulletin, 23, 259–272.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1996). Reinsurance and ruin. Insurance: Mathematics & Economics, 19, 61–80.Google Scholar
Dimitrova, D.S. & Kaishev, V.K. (2010). Optimal joint survival reinsurance: an efficient frontier approach. Insurance: Mathematics & Economics, 47, 27–35.Google Scholar
Dufresne, F., Gerber, H.U. & Shiu, E.S.W. (1991). Risk theory and the gamma process. ASTIN Bulletin, 21, 177–192.CrossRefGoogle Scholar
Hesselager, O. (1990). Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal, 1990, 80–95.CrossRefGoogle Scholar
Hipp, C. & Vogt, M. (2003). Optimal dynamic XL reinsurance. ASTIN Bulletin, 33, 193–207.CrossRefGoogle Scholar
Hosseini, S.-H., Ezazi, M.E., Heshmati, M.R. & Moghadam, S.-M.R.H. (2013). Top companies ranking based on financial ratio with AHP-TOPSIS combined approach and indices of Tehran stock exchange – a comparative study. International Journal of Economics and Finance, 5, 126–133.Google Scholar
Hürlimann, W. (2011). Optimal reinsurance revisited – point of view of cedent and reinsurer. ASTIN Bulletin, 41, 547–574.Google Scholar
Hwang, C.L. & Yoon, K.P. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer Verlag, New York.CrossRefGoogle Scholar
Kim, G., Park, C.S. & Yoon, K.P. (1997). Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement. International Journal of Production Economics, 50, 23–33.Google Scholar
Mahalanobis, P.C. (1936). On the generalised distance in statistics. Proceedings of the National Institute of Sciences of India, 2, 49–55.Google Scholar
Rao, R.V. (2007). Decision Making in the Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods. Springer, London.Google Scholar
Schmidli, H. (2004). Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: the large claim case. Queueing Systems, 46, 149–157.Google Scholar
Velasquez, M. & Hester, P.T. (2013). An analysis of multi-criteria decision making methods. International Journal of Operations Research, 10, 56–66.Google Scholar
Waters, H.R. (1983). Some mathematical aspects of reinsurance. Insurance: Mathematics & Economics, 2, 17–26.Google Scholar
Wu, D. & Olson, D.L. (2006). A TOPSIS data mining demonstration and application to credit scoring. International Journal of Data Warehousing and Mining, 2, 16–26.CrossRefGoogle Scholar