應用隨機過程分析人身保險之提前給付計畫

     

 

: NSC 87-2118-M-004-003

:
  

 : 868187731

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01234-56 789:;<=>?@AB$  !CDEFGHIJKLMN NOIPQR:STUVWXR : Wolthuis (1987)YWXZ[\]5 678UV^_`ab\c*de fghijklmnopq0567 8r&st=>uvwKxyz0 1234E6{|%&$}~^r&  !€H‚opq0ƒ „;st…V<=>AB$ !K †w !‡          Abstract

Profit analysis is an essential procedure in testing and measuring the new life insurance product prior to be sold in the market. Facing nowaday complicated insurance products, the traditional actuarial models need to be generalized. In this paper, we adopt the Markov chain methodology in formulating the stochastic phenomena in the multi-state accelerated benefit insurance plan. Disability and AIDS insurance are utilized to illustrate the modeling procedure. Time-inhomogeneous Markov chain model

in Wolthuis (1987) is implemented and a typical annuity product discussed in Ramlau-Hansen (1988) is used for analysis. Transition probabilities within various states adjusted for current information are incorporated in computing the reserves and the surplus at different insured age. Using the methodology of stochastic process in modeling the transition pattern within various states could be beneficial to the insurers in managing the financial risks. The proposed approach is believed to be crucial in developing more enhanced life insurance and annuity portfolios in the future.

Keyword: Markov chain, multi-state accelerated benefit plan.

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(x=40,y=35)    !"#$% & '( x )* y )+,-./ 0 Gompertz 1 %  2 ! 3456'( 7
89:(w);<=%>?(x,y) @<=%81A Bowers(1986)BCD EFG%HIJK@<=%(multiple life functions)I LMNc=1.084766, x=40, y=35 O8PQRST w=46UV N*WGXYZWG 3[\]^_WG`a8bcd7e fg81Ahij1995k 1. lm9nWGopqU 2. WGrOs t O  V<sub>1</sub>(t), V<sub>2</sub>(t), V<sub>3</sub>(t), V<sub>4</sub>(t)U 3. WGrOs t O  R<sub>12</sub>(t), R<sub>13</sub>(t), R<sub>24</sub>(t)U 4. WGt<sub>12</sub>(u), t<sub>13</sub>(u), t<sub>24</sub>(u)!t(u)U vWwxyz{ |}~Y9:€8‚ƒ„…† ‡ˆ ‰Š89:W%`a ‰Š‹ŒbcŽ…/‘ l’*“”•<n–—D˜< ™š`€8‚ƒ•›œy žr†Ÿ ‡ˆC¡‰Š¢£` aU¤ ¤ ¤ ¥1A}¦¤ ¤ ¤ 1.hij§:‹Œ`a…¡ ‰Š ¡ ¨©I102ª«¬8412­U 2.Bowers, N. L., H. U. Gerber, J. C.

Hickman, D. A. Jones and C. J. Nesbitt

(1986). Actuarial Mathematics. The Society of Actuaries, Itasca, IL.

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Deutschen Gesellschaft Versicherungsmathematik IX, 91-107.

4.Hoem, J. M. and O. O. Aalen (1978). Actuarial values of payment streams. Scandinavian Actuarial Journal 61, 38-47. 5.Panjer, H. H. (1988). AIDS: Survival

Analysis of Persons Testing HIV + TSA XL, Part I, 517-30.

6.Ramlau-Hansen, H. (1988). Hattendroff's Theorem: A Markov Chain and Counting Process Approach, Scandinavian Actuarial Journal 71, 143-156.

7.Ramlau-Hansen, H. (1988). The emergence of profit in life insurance, Insurance: Mathematics and Economics 7, 225-236. 8.Ramsay, C. M. (1989). AIDS and the

Calculation of Life Insurance Functions, TSA XLI, 392-422.

9.Tolley, H. D. and Manton, K. G. (1991). Intervention Effects amonga Collection of Risks, TSA XLIII, 117-42.

10.Waters, H. R. (1990). The Recursive Calculation of the Moments of the Profit on a Sickness Insurance Policy, Insurance: Mathematics and Economics 9, 101-13. 11.Wolthuis, H. (1987). Hattendroff's

theorem for a continuous-time Markov model. Scandinavian Actuarial Journal 70, 157-175.