Balbás, Alejandro and Balbás, Beatriz and Heras, Antonio (2008) Optimal Reinsurance Wtih General Risk Functions. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
The paper studies the optimal reinsurance problem if the risk level is measured by a general risk function. Necessary and sufficient optimality conditions are given
for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Then the optimality conditions are used to verify whether the classical reinsurance contracts (quota-share, stop-loss) are optimal regardless of the risk function to be used, and the paper ends by particularizing the findings so as to study in detail two deviation measures and the Conditional Value at Risk.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Balbás, Alejandro and Balbás, Beatriz and Heras, Antonio|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 3/08|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Optimal reinsurance, Risk measure and deviation measure, Optimality conditions|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||03 Jun 2010 20:08|
|Last Modified:||08 Dec 2010 23:19|
Alexander, S., T.F. Coleman and Y. Li, 2006. “Minimizing CV aR and V aR for a portfolio of derivatives”. Journal of Banking & Finance, 30, 538-605.
Anderson, E.J. and P. Nash, 1987. “Linear programming in infinite-dimensional spaces”. John Wiley & Sons, New York.
Arrow, K. J., 1963. “Uncertainty and the welfare of medical care”. American Economic Review, 53, 941-973.
Artzner, P., F. Delbaen, J.M. Eber and D. Heath, 1999. “Coherent measures of risk”. Mathematical Finance, 9, 203-228.
Balbás, A., R. Balbás and S. Mayoral, 2008. “Portfolio choice problems and optimal hedging with general risk functions: A simplex-like algorithm”. European Journal of Operational Research (forthcoming).
Balbás, A. and R. Romera, 2007. “Hedging bond portfolios by optimization in Banach spaces”. Journal of Optimization Theory and Applications, 132, 1, 175-191.
Borch, K. (1960) “An attempt to determine the optimum amount of stop loss reinsurance”. Transactions of the 16th International Congress of Actuaries I, 597-610.
Burgert, C. and L. Rüschendorf, 2006. “Consistent risk measures for portfolio vectors”. Insurance: Mathematics and Economics, 38, 2, 289-297.
Cai, J. and K.T. Tan, 2007. “Optimal retention for a stop loss reinsurance under the V aR and CTE Risk Measures”. ASTIN Bulletin, 37, 1, 93-112.
Cherny, A.S., 2006. “Weighted V@R and its properties”. Finance & Stochastics, 10, 367-393.
Frittelli, M. and G. Scandolo, 2005. “Risk measures and capital requirements for processes”. Mathematical Finance, 16, 4, 589-612.
Gajec, L. and D. Zagrodny, 2004. “Optimal reinsurance under general risk measures”. Insurance: Mathematics and Economics, 34, 227-240.
Goovaerts, M., R. Kaas, J. Dhaene and Q. Tang, 2004. “A new classes of consistent risk measures”. Insurance: Mathematics and Economics, 34, 505-516.
Horvàth, J., 1966. “Topological vector spaces and distributions, vol I” Addison Wesley, Reading, MA.
Kaluszka, M. 2001. “Optimal reinsurance under mean-variance premium principles”. Insurance: Mathematics and Economics, 28, 61-67.
Kaluszka, M. 2005. “Optimal reinsurance under convex principles of premium calculation”. Insurance: Mathematics and Economics, 36, 375-398.
Konno, H., K. Akishino and R. Yamamoto, 2005. “Optimization of a long-short portfolio under non-convex transaction costs”. Computational Optimization and Applications, 32, 115-132.
Luenberger, D.G.,1969. “Optimization by vector spaces methods”. John Wiley & Sons, New York.
Mansini, R., W. Ogryczak and M.G. Speranza, 2007.
“Conditional value at risk and related linear programming models for portfolio optimization”. Annals of Operations Research, 152, 227-256
Nakano, Y., 2004. “Efficient hedging with coherent risk measure”. Journal of Mathematical Analysis and Applications, 293, 345-354.
Ogryczak, W. and A. Ruszczynski, 1999. “From stochastic dominance to mean risk models: Semideviations and risk measures”. European Journal of Operational Research, 116, 33-50.
Ogryczak,W. and A. Ruszczynski, 2002. “Dual stochastic dominance and related mean risk models”. SIAM Journal of Optimization, 13, 60-78.
Rockafellar, R.T., S. Uryasev and M. Zabarankin, 2006.
“Generalized deviations in risk analysis”. Finance & Stochastics, 10, 51-74.
Schied, A. 2007. “Optimal investments for risk- and ambiguity-averse preferences: A duality approach”. Finance & Stochastics, 11, 107-129.
Wang, S.S., 2000. “A class of distortion operators for pricing financial and insurance risks”. Journal of Risk and Insurance, 67, 15-36.
Young, V. R. 1999. “Optimal insurance under Wang’s premium principle”. Insurance: Mathematics and Economics, 25, 109-122.
Zalinescu, C., 2002. “Convex analysis in general vector spaces”. World Scientific Publishing Co.
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