tel-00703797, version 2 - 7 Jun 2012 Chapitre 2. Theorie <strong><strong>de</strong>s</strong> jeux et cycles <strong>de</strong> marché Markham, F. J. (2007), An investigation into un<strong>de</strong>rwriting cycles in the South African shortterm insurance market for the period 1975 to 2006, Technical report, University of the Witwatersrand. 94 Marshall, A. W. and Olkin, I. (1979), Inequalities: theory of majorization and its applications, Aca<strong>de</strong>mic Press. 130, 131 McFad<strong>de</strong>n, D. (1981), Econometric Mo<strong>de</strong>ls of Probabilistic Choice, in ‘Structural Analysis of Discrete Data with Econometric Applications’, The MIT Press, chapter 5. 96 Mimra, W. and Wambach, A. (2010), A Game-Theoretic Foundation for the Wilson Equilibrium in Competitive Insurance Markets with Adverse Selection. CESifo Working Paper No. 3412. 95 Moreno-Codina, J. and Gomez-Alvado, F. (2008), ‘Price optimisation for profit and growth’, Towers Perrin Emphasis 4, 18–21. 95 Osborne, M. and Rubinstein, A. (2006), A Course in Game Theory, Massachusetts Institute of Technology. 101, 115 Picard, P. (2009), Participating insurance contracts and the Rothschild-Stiglitz equilibrium puzzle. working paper, Ecole Polytechnique. 94, 95 Polborn, M. K. (1998), ‘A mo<strong>de</strong>l of an oligopoly in an insurance market’, The Geneva Paper on Risk and Insurance Theory 23(1), 41–48. 95 Powers, M. R. and Shubik, M. (1998), ‘On the tra<strong>de</strong>off between the law of large numbers and oligopoly in insurance’, Insurance: Mathematics and Economics 23(2), 141–156. 95 Powers, M. R. and Shubik, M. (2006), ‘A “square- root rule” for reinsurance’, Cowles Foundation Discussion Paper No. 1521. . 95 R Core Team (2012), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org 104 Rees, R., Gravelle, H. and Wambach, A. (1999), ‘Regulation of insurance markets’, The Geneva Paper on Risk and Insurance Theory 24(1), 55–68. 95 Rockafellar, R. T. and Wets, R. J.-V. (1997), Variational Analysis, Springer-Verlag. 109 Rosen, J. B. (1965), ‘Existence and Uniqueness of Equilibrium Points for Concave N-person Games’, Econometrica 33(3), 520–534. 102, 110 Rothschild, M. and Stiglitz, J. E. (1976), ‘Equilibrium in competitive insurance markets: An essay on the economics of imperfect information’, The Quarterly Journal of Economics 90(4), 630–649. 94 Shaked, M. and Shanthikumar, J. G. (2007), Stochastic Or<strong>de</strong>rs, Springer. 120, 129, 130 Shapley, L. (1953), ‘Stochastic games’, Proc. Nat. Acad. Sci. U.S.A. 39(10), 1095–1100. 115 134
tel-00703797, version 2 - 7 Jun 2012 BIBLIOGRAPHY Sigmund, K. and Hofbauer, J. (1998), Evolutionary Games and Population Dynamics, Cambridge University Press. 115 Taksar, M. and Zeng, X. (2011), ‘Optimal <strong>non</strong>-proportional reinsurance control and stochastic differential games’, Insurance: Mathematics and Economics 48(1), 64–71. 95 Taylor, G. C. (1986), ‘Un<strong>de</strong>rwriting strategy in a competitive insurance environment’, Insurance: Mathematics and Economics 5(1), 59–77. 95, 124 Taylor, G. C. (1987), ‘Expenses and un<strong>de</strong>rwriting strategy in competition’, Insurance: Mathematics and Economics 6(4), 275–287. 95, 124 Trufin, J., Albrecher, H. and Denuit, M. (2009), ‘Impact of un<strong>de</strong>rwriting cycles on the solvency of an insurance company’, North American Actuarial Journal 13(3), 385–403. 95 Venezian, E. C. (1985), ‘Ratemaking methods and profit cycles in property and liability insurance’, Journal of Risk and Insurance 52(3), 477–500. 94 von Heusinger, A. and Kanzow, C. (2009), ‘Optimization reformulations of the generalized Nash equilibrium problem using the Nikaido-Isoda type functions’, Computational Optimization and Applications 43(3). 110 Wambach, A. (2000), ‘Introducing heterogeneity in the Rothschild-Stiglitz mo<strong>de</strong>l’, Journal of Risk and Insurance 67(4), 579–591. 95 Zorich, V. (2000), Mathematical Analysis I, Vol. 1, Universitext, Springer. 124 135
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