Generalized Optimized Certainty Equivalent with Applications in the Rank-Dependent Utility Model

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-03-26 DOI:10.1137/21m1448276

Qinyu Wu, Tiantian Mao, Taizhong Hu

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引用次数: 0

Abstract

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 255-294, March 2024.
Abstract. The classic optimized certainty equivalent (OCE), proposed by Ben-Tal and Teboulle [Manag. Sci., 11 (1986), pp. 1445–1466], employs the classical expected utility model to evaluate the random risk, in which model each decision maker is characterized by a unique probability measure and only outcome uncertainty is assumed. Due to the lack of information, the distribution ambiguity or Knightian uncertainty prevails in reality. We employ the variational preference of Maccheroni, Marinacci, and Rustichini [Econometrica, 74 (2006), pp. 1447–1498] to address the issue and generalize the concept of OCE. In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on [math]-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of the RDU-based shortfall risk measure proposed by Mao and Cai [Finance Stoch., 2 (2018), pp. 367–393] is also presented.

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广义优化确定性等价物在等级相关效用模型中的应用

SIAM 金融数学期刊》，第 15 卷第 1 期，第 255-294 页，2024 年 3 月。摘要。Ben-Tal 和 Teboulle [Manag. Sci.，11 (1986)，pp.1445-1466]提出的经典优化确定性等价（OCE）采用经典期望效用模型来评估随机风险。由于缺乏信息，现实中普遍存在分布模糊性或奈特不确定性。我们采用 Maccheroni、Marinacci 和 Rustichini [Econometrica, 74 (2006), pp.在本文中，我们介绍了一类基于变分偏好的优化确定性等价物，给出了其基于[math]-发散的对偶表示，并研究了其正同质性和一致性的等价表征。作为应用，我们研究了基于等级依赖效用（RDU）模型的优化确定性等价物的特性。还介绍了毛和蔡提出的基于 RDU 的亏空风险度量的对偶表示[Finance Stoch.，2 (2018)，第 367-393 页]。

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.