Volume 20, Issue 1 (6-2021)                   JIRSS 2021, 20(1): 183-196 | Back to browse issues page


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Fathi Manesh S, Izadi M, Khaledi B. Some New Results on Policy Limit Allocations. JIRSS. 2021; 20 (1) :183-196
URL: http://jirss.irstat.ir/article-1-781-en.html
Department of Statistics, University of Kurdistan, Sanandaj, Iran , sirus_60@yahoo.com
Abstract:   (602 Views)

Suppose that a policyholder faces $n$ risks X1, ..., Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that ∑ni=1li=l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, we prove that the equal limits provide the maximum of the expected utility of the wealth of policyholder. If the risks with log-concave distribution functions are independent and ordered in the sense of the reversed hazard rate order, we show that the equal limits is the most favourable allocation among the worst allocations. We also prove that if the joint probability density function is arrangement increasing, then the best arranged allocation maximizes the utility expectation of policyholder's wealth. We apply the main results to the case when the risks are distributed according to a log-normal distribution.

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Type of Study: Special Issue, Original Paper | Subject: 62Exx: Distribution theory
Received: 2020/12/6 | Accepted: 2021/02/21 | Published: 2021/06/20

References
1. Cheung, K. C. (2007), Optimal allocation of policy limits and deductibles. Insurance: Mathematics and Economics, 41, 382-391. [DOI:10.1016/j.insmatheco.2006.11.010]
2. Denuit, M., and Vermandele, C. (1998), Optimal reinsurance and stop loss order. Insurance: Mathematics and Economics, 22, 229-233. [DOI:10.1016/S0167-6687(97)00039-5]
3. Denuit, M., Dhaene, J., Goovaerts, M. J., and Kaas, R. (2005), Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley & Sons, New york.
4. Hollander, M., Proschan, F., and Sethuraman, J. (1977), Functions decreasing in transposition and their applications in ranking problems. The Annals of Statistics, 5, 722-733. [DOI:10.1214/aos/1176343895]
5. Hua, L., and Cheung, K. C. (2008), Stochastic orders of scalar products with applications. Insurance: Mathematics and Economics, 42, 865-872. [DOI:10.1016/j.insmatheco.2007.10.004]
6. Hu, S., and Wang, R. (2014), Stochastic comparisons and optimal allocation for policy limits and deductibles. Communications in Statistics-Theory and Methods, 43, 151-164.
7. Kaas, R., Goovaerts, M., Dhaene, J., and Denuit, M. (2008). Modern actuarial risk theory: using R. Springer Science & Business Media.
8. Klugman, S., Panjer, H., and Willmot, G. (2004), Loss Models: From Data to Decisions, second ed. John Wiley & Sons, New Jersey.
9. Lu, Z., and Meng, L. (2011), Stochastic comparisons for allocations of policy limits and deductibles with applications. Insurance: Mathematics and Economics, 48, 338-343.
10. Manesh F. S., and Khaledi, B. E. (2015), Allocations of policy limits and ordering relations for aggregate remaining claims. Insurance: Mathematics and Economics, 65, 9-14. [DOI:10.1016/j.insmatheco.2015.08.003]
11. Marshall, A. W., Olkin, I., and Arnold, B. C. (2011), Inequalities: Theory of Majorization and its Applications. Springer, New York.
12. M"uller, A., and Stoyan, D. (2002), Comparison Methods for Stochastic Models and Risks. John Wiley & Sons, New York.
13. Pecaric, J. E., Proschan, F., and Tong, Y. L. (1992), Convex functions, partial orderings, and statistical applications. Academic Press, Inc. San Diego.
14. Shaked, M., and Shanthikumar, J. G. (2007), Stochastic Orders. Springer, New York.
15. Heerwaarden, A. E., Kaas, R., and Goovaerts, M. J. (1989), Optimal reinsurance in relation to ordering of risks. Insurance: Mathematics and Economics, 8, 11-17. [DOI:10.1016/0167-6687(89)90041-3]

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