Fair split of profit generated by n parties
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DOIhttp://dx.doi.org/10.21511/ins.09(1).2018.01
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Article InfoVolume 9 2018, Issue #1, pp. 1-5
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The authors studied the process of merging insured groups, and the splitting of the profit that arises in the process due to the fact that the risk for the merged group is essentially reduced. There emerges a profit and there are various ways of splitting this profit between the combined groups. Techniques from game theory, in particular cooperative game theory turn out to be useful in splitting of the profit. The authors proceed in this paper to apply techniques of utility theory to study the possibility of a fair split of that profit. In this research, the authors consider a group of n parties 1,...,n such that each of them has a corresponding utility function u1(x),...,un(x) . Given a positive amount of money C, a fair split of C is a vector (c1,...,cn) in Rn, such that c1 +...cn = C and u1(c1) = u2(c2) = ... = un(cn). The authors presume the utility functions to be normalized, that is ui(c) = 1 for each party i, i = 1, ... ,n. The authors show that a fair split exists and is unique for any given set of utility functions u1(x), ..., un(x), and for any given amount of money C. The existence theorem follows from observing simplexes. The uniqueness follows from the utility functions being strictly increasing. An example is given of normalizing some utility functions, and evaluating the fair split in special cases. In this article, the authors study the case of merging two groups (or more) of insured members, they provide an evaluation of the emerging benefit in the process, and the splitting of the benefit between the groups.
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JEL Classification (Paper profile tab)C51, C57
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References14
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- Borch, K. (1974). The Mathematical Theory of Insurance. D.C. Heath & Company.
- Brower, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1997). Actuarial Mathematics. The Society of Actuaries.
- Conitzer, V., Sandholm, T. (2004). Computing Shapley values, manipulating value division schemes, and checking core membership in multi-issue domains. In Proceedings of the National Conference on Artificial Intelligence (AAAI), 219-225.
- Date, P., Mamon, R., Wang, I. C. (2007). Valuation of cash flows under random rates of interest: A linear algebraic approach. IME, 41, 84-95.
- Kahneman, D., Tversky, A. (1979). Prospect Theory: An Analysis of Decision Under Risk. Econometrica, 47(2), 263-291.
- Knaster, B., Kuratowski, C., Mazurkiewicz, C., & des Lebens, E. B. (1929). Fixpunktsatzes fuer n-dimensionale Simplexe. Fundamenta Mathematicae, 14, 132-137.
- Lemaire, J. (1979). Reinsurance as a Cooperative Game. Game Theory and Applications, 254-269.
- McCutcheon, J. J., Scott, W. F. (1991). An Introduction to the Mathematics of Finance. Butterworth-Heinemann, Oxford.
- Mualem, E., Zaks, A. (2017). Joining insured groups: how to split the emerging profit. Insurance Markets and Companies, 8(1), 29-33.
- Neill, A. (1989). Life contingencies. Heinemann Pro. Pub. Oxford.
- Shapley, L. S. (1929). Cores of Convex Games. International Journal of Game Theory, 1, 11-26.
- Zaks, A. (2001). Annuities under random rates of interest. Insurance: Mathematics and Economics, 28, 1-11.
- Zaks, A. (2009). Annuities under changes in Life Tables and changes in the Interest. The Journal of Insurance and Risk Management, 8, 47-52.
- Zaks, A. (2010). Annuities Under Random Rates of Interest II. The Journal of Insurance and Risk Management, 5(2), 59-65.