HOME> 논문 > 논문 검색상세

## 논문 상세정보

### 구간치 쇼케이적분과 위험률 가격 측정에서의 응용 Interval-valued Choquet integrals and applications in pricing risks

장이채    (건국대학교 컴퓨터응용과학부 전산수학  );
• #### 초록

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}1,\;{\mu}2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• #### 주제어

Choquet integrals .   non-additive measures .   interval-valued risks .   updated prices.

• #### 참고문헌 (15)

1. J. Aubin, 'Set-valued analysis', Birkauser Boston, 1990
2. R.J. Aumann, 'Integrals of set-valued functions', J. Math. Anal. Appl. 12 (1965), 1-12
3. Jean-Luc Marichal, Tolerant or intorant character of interacting criteria in aggregation by the Choquet integral, European J. of Operational Research 155(2004), 771-791
4. D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97(1986), 253-261
5. L. C. Jang and J. S. Kwon, On the representation of Choquet integrals of set-valued functions and null sets, Fuzzy Sets and Systems 112(2000), 233-239
6. A.De Waegenare, R.Kast, and A.Laped, Choquet pricing and equilibrium, Insurance; Mathematics and Economics 32(2003), 359-370
7. T. Murofushi and M. Sugeno, A theory of Fuzzy measures: representations, the Choquet integral, and null sets, J. Math. Anal. and Appl. 159(1991), 532-549
8. V.R. Young, Families of update rules for non-additive measures; Applications in pricing risks, Insurance; Mathematics and Economics 23 (1998), 1-14
9. L.C. Jang, Some characterizations of interval- valued Choquet price functionals, J. of Fuzzy Logic and Intelligent Systems 16(2) (2006), 247-251
10. A.De Waegenare and P. Wakker, Nonmonotonic Choquet integrals, J. of Mathematical Economics 36(2001), 45-60
11. L.C. Jang, T. Kim and J.D. Jeon, On set-valued Choquet integrals and convergence theorems (II), Bull. Korean Math. Soc. 40(1) (2003), 139-147
12. L.C.Jang, B.M.Kil, Y.K.Kim and J.S.Kwon, Some properties of Choquet integrals of set-valued functions, Fuzzy Sets and Systems 91(1997), 61-67
13. S.S.Wang, V.R.Young, and H.H. Panjer, Axiomatic characterizations of insurance prices, Insurance; Mathematics and Economics 21 (1997), 173-183
14. L.C. Jang, Interval-valued Choquet integrals and their applications, J. Appl, Math. & Computing 16(1-2) (2004), 429-443
15. D. Zhang, C. Guo and D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems 147 (2004), 475-485
• #### 이 논문을 인용한 문헌 (4)

1. Jang, Lee-Chae ; Kim, Tae-Kyun ; Kim, Young-Hee 2008. "Choquet weak convergence for interval-valued capacity functionals of random sets" 한국지능시스템학회 논문지 = Journal of Korean institute of intelligent systems, 18(6): 837~841
2. Jang, Lee-Chae ; Kim, Tae-Kyun 2009. "A study on interval-valued necessity measures through the Choquet integral criterian" 한국지능시스템학회 논문지 = Journal of Korean institute of intelligent systems, 19(3): 350~354
3. 2009. "" International journal of fuzzy logic and intelligent systems : IJFIS, 9(2): 71~75
4. Jang, Lee-Chae ; Kim, Tae-Kyun ; Kim, Hyun-Mee 2010. "A note on Linguistic quantifiers modeled by Sugeno integral with respect to an interval-valued fuzzy measures" 한국지능시스템학회 논문지 = Journal of Korean institute of intelligent systems, 20(1): 1~6

저자의 다른 논문

• #### 장이채 (46)

1. 2001 "L-R 퍼지수의 집합-이론적 연산과 제2형 퍼지집합의 기수" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 11 (2): 115~118
2. 2001 "퍼지수행평가방법과 수학교육" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 11 (8): 742~745
3. 2003 "A note on fuzzy knowledge spaces" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 13 (1): 97~101
4. 2003 "평가부분에서 지식공간과 퍼지이론의 활용 방안에 관한 연구" 韓國學校數學會論文集 = Journal of the Korean school mathematics society 6 (1): 27~43
5. 2003 "중학 수학의 연계적인 교수 학습 방법에 관한 연구 - 함수 영역을 중심으로" 韓國學校數學會論文集 = Journal of the Korean school mathematics society 6 (2): 21~37
6. 2003 "탐구형 소프트웨어를 이용한 학습 환경에서 학생들의 기하 개념의 이해" 한국수학교육학회지. 시리즈 E: 수학교육논문집 16 (): 93~108
7. 2004 "ON FUZZY INTEGRALS DEFINED BY MAX-MEASURES" Honam mathematical journal = 호남수학학술지 26 (3): 355~364
8. 2004 "INTERVAL-VALUED CHOQUET INTEGRALS AND THEIR APPLICATIONS" Journal of applied mathematics & computing 16 (1): 429~443
9. 2005 "GENERALIZED NET MODEL OF INTRANET IN AN ABSTRACT UNIVERSITY WITH CURRENT ESTIMATIONS (II)" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 15 (3): 382~388
10. 2005 "q-ANALOGUE OF EULER-BARNES' NUMBERS AND POLYNOMIALS" Bulletin of the Korean Mathematical Society = 대한수학회보 42 (3): 491~499

활용도 분석

amChart 영역

amChart 영역

#### 원문보기

##### 유료다운로드

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기