JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (07): 57-62.doi: 10.6040/j.issn.1671-9352.0.2014.106

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Extremal distributions for 5-convex stochastic orderings with arbitrary discrete support and applications in actuarial sciences

TIAN You-gong, LIU Zhuan-ling   

  1. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China
  • Received:2014-03-20 Online:2014-07-20 Published:2014-09-15

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Abstract: In the sense of discrete 5-convex stochastic ordering, the extremal distribution for random variables valued in an arbitrary discrete subset of the half-positive real line R+ was considered. The bounds of Lundberg's adjustment coefficient in actuarial sciences were estimated.

Key words: arbitrary support, extremal distribution, s-convex stochastic orderings, Lundberg's adjustment coefficient

CLC Number: 

  • O211.6
[1] KAAS R, VAN HEERWAARDEN A E, GOOVAERTS M. Ordering of actuarial risks[M]. Brussels: CAIRE, 1994.
[2] SHAKED M, SHANTHIKUMAR J G. Stochastic orders and their applications[M]. New York: Springer, 2006.
[3] DENUIT M, DHAENE J, GOOVAERTS M, et al. Actuarial theory for dependent risks: measures, orders and models[M]. New York: Wiley, 2005.
[4] FISHBURN P C, LAVALLE I H. Stochastic dominance on unidimensional grids[J]. Mathematics of Operations Research,1995, 20(3):513-525.
[5] DENUIT M, LEFVRE C L. Some new classes of stochastic order relations among arithmetic random variables with applications in actuarial sciences[J]. Insurance: Mathematics and Economics, 1997, 20(3):197-214.
[6] DENUIT M, LEFVRE C L, MESFIOUI M. On s-convex stochastic extrema for arithmetic risks[J]. Insurance: Mathematics and Economics, 1999, 25(2):143-155.
[7] COURTOIS C, DENUIT M, BELLEGEM S V. Discrete s-convex extremal distributions: Theory and applications[J]. Applied Mathematics Letters, 2006, 19(12):1367-1377.
[8] 田有功,焦桂梅.离散的5阶凸随机序的极值分布及其应用[J].山东大学学报:理学版, 2014, 49(1):99-104.
[9] DENUIT M, LEFVRE C L, UTEV S. Stochastic orderings of convex/concave type on an arbitrary grid[J]. Mathematics of Operations Research, 1999, 24(4):835-846.
[10] COURTOIS C, DENUIT M. S-convex extremal distributions with arbitrary discrete support[J]. Journal of Mathematical Inequalities, 2008, 2(2):197-214.
[11] DENUIT M, LEFVRE C L, SHAKED M. The s-convex orders among real random variables with applications[J]. Mathematical Inequalities and Applications, 1998, 1(4):585-613.
[12] SHIU E S W. The probability of eventual ruin in the compound binomial model[J]. Astin Bulletin, 1989, 19(2):179-190.
[13] WILLMOT G E. Ruin probabilities in the compound binomial model[J]. Insurance: Mathematics and Economics, 1993, 12(2):133-142.
[14] WALHIN J F, PARIS J. On the use of equispaced discrete distributions[J]. Astin Bulletin, 1998, 28(2):241-255.
[1] TIAN You-gong1, JIAO Gui-mei2*. Extremal distribution for the discrete 5-convex stochastic #br# ordering and applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(1): 99-104.
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