具有随机区间收益的效用优化分析

数学季刊 ›› 2012, Vol. 27 ›› Issue (3): 424-431.

具有随机区间收益的效用优化分析

College of Science, Donghua University

收稿日期:2011-01-16 出版日期:2012-09-30 发布日期:2023-03-24
作者简介:YOU Su-rong(1976-), male, native of Jingjiang, Jiangsu, an associate professor of Donghua University, M.S.D., engages in mathematical ﬁnance; PENG Yu-zhen(1985-), male, native of Hengyang, Hunan,a graduate of Donghua University, engages in mathematical ﬁance; ZHAO Fei-fei(1984-), female, native of Linyi, Shandong, a graduate of Donghua University, engages in mathematical ﬁance.
基金资助:
Supported by the Fundamental Research Funds for the Central University(10D10909)

On Utility Maximization with Random Interval Payoﬀs

College of Science, Donghua University

Received:2011-01-16 Online:2012-09-30 Published:2023-03-24
About author:YOU Su-rong(1976-), male, native of Jingjiang, Jiangsu, an associate professor of Donghua University, M.S.D., engages in mathematical ﬁnance; PENG Yu-zhen(1985-), male, native of Hengyang, Hunan,a graduate of Donghua University, engages in mathematical ﬁance; ZHAO Fei-fei(1984-), female, native of Linyi, Shandong, a graduate of Donghua University, engages in mathematical ﬁance.
Supported by:
Supported by the Fundamental Research Funds for the Central University(10D10909)

摘要/Abstract

摘要： This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor’s subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets’ prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.

关键词: random interval payoff acceptable state price vector, expected utility, optimal strategy

Abstract: This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor’s subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets’ prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.

Key words: random interval payoff, acceptable state price vector, expected utility, optimal strategy

中图分类号:

尤苏蓉, 彭玉争, 赵菲菲. 具有随机区间收益的效用优化分析[J]. 数学季刊, 2012, 27(3): 424-431.

YOU Su-rong, PENG Yu-zheng, ZHAO Fei-fei. On Utility Maximization with Random Interval Payoﬀs[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(3): 424-431.