鲁棒信用风险优化的线性锥优化模型

运筹学学报 ›› 2013, Vol. 17 ›› Issue (1): 86-97.

鲁棒信用风险优化的线性锥优化模型

张弘捷¹，白延琴¹，方淳亮¹

1. 上海大学数学系

出版日期:2013-03-15 发布日期:2013-03-15
通讯作者: 白延琴 E-mail:yqbai@shu.edu.cn

Linear conic optimization models for robust credit risk optimization

ZHANG Hongjie¹, BAI Yanqin¹, FANG Chunliang¹

1. Department of Mathematics, Shanghai University

Online:2013-03-15 Published:2013-03-15

摘要/Abstract

摘要： 考虑了具有强健性的信用风险优化问题. 根据最差条件在值风险度量信用风险的方法，建立了信用风险优化问题的模型. 由于信用风险的损失分布存在不确定性，考虑了两类不确定性区间，即箱子型区间和椭球型区间. 把具有强健性的信用风险优化问题分别转化成线性规划问题和二阶锥规划问题. 最后，通过一个信用风险问题的例子来说明此模型的有效性.

关键词: 信用风险优化, 最差在值风险, 线性优化, 二阶锥优化

Abstract: In this paper we deal with the credit risk optimization problem. We present a model based on the worst-case Conditional Value-at-Risk (CVaR) risk measure and the uncertainty for the credit risk loss distribution. Under the box uncertainty, we reformulate the model into a linear optimization problem. Furthermore, under the ellipsoidal uncertainty, we reformulate the model into a seconde-order cone optimization problem. Finally, we show a numerical example to demonstrate the effective of our models.

Key words: credit risk optimization, worst-case CVaR, linear optimization, second-order cone optimization

张弘捷，白延琴，方淳亮. 鲁棒信用风险优化的线性锥优化模型[J]. 运筹学学报, 2013, 17(1): 86-97.

ZHANG Hongjie, BAI Yanqin, FANG Chunliang. Linear conic optimization models for robust credit risk optimization[J]. Operations Research Transactions, 2013, 17(1): 86-97.

参考文献

Ghaoui L, Oustry F. Worst-case Value-at-Risk and robust portfolio optimization: A conic programming approach [J]. Operations Research, 2003, 51: 543-556.
Markowitz H M. Portfolio selection [J].   Journal of Finance, 1952, 7: 77-91.
Rockafellar R T, Uryasev S. Optimization of conditional Value-at-Risk [J]. Journal of Risk, 2000, 2: 21-41.
Lobo M, Fazel M, Boyd S. Portfolio optimization with linear and fixed transaction costs [J]. Annals of Operations Research, 2007, 152(1): 376-394.
Artzner P, Delbaen F, Eber J M, et al. Coherence measuresof risk [J]. Mathematical Finance, 1999, 9: 203-228.
Lobo M S, Vandenberghe L, Boyd S. Applications of second-order cone programming [J].   Linear Algebra and its Applications, 1998, 284: 193-228.
Pflug G. Some remarks on the Value-at-Risk and conditional Value-at-Risk [M]// Proba-bilistic Constrained Optimization: Methodology and Applications, Dordrecht: Ed. S. Uryasev, Kluwer Academic Publishers, 2002.
Rockafellar R T, Uryasev S. Conditional Value-at-Risk for general loss distributions [J].   Journal of Banking and Finance, 2002,

26: 1443-1471.
Andersson F, Mausser H. Credit risk optimization with Conditional Value-at-Risk criterion [J]. Math.Program, 2001, 89: 273-291.
Saunders D, Xiouros C. Credit risk optimization using factor models [J]. Ann Oper Res, 2007, 152: 49-77.
Costa O, Paiva A. Robust porfolio selection using linear-matrix inequality [J].   Journal of Ecnomic Dynamics Control, 2002, 26: 889-909.
Goldfarb D, Iyengar G. Robust portfolio selection problems [J]. Mathematics of Operations Research, 2003, 28: 1-38.
Zhu S S, Fukushima M. Worst-case conditional Value-at-Risk with application to robust portfolio management [J]. Operations Research, 2009, 57: 1155-1168.
RiskMetrics Technical Document [R]. New York: J P Morgan Inc, 1996.
Black F, Litterman R. Global portfolio optimization [J].    Financial Analysts Journal, 1992, 48: 28-43.
Ben-Tal A, Nemirovski A. Robust optimization methodology and applications [J]. Mathematical Programming (Ser. B), 2002, 92: 453-480.

[1]	徐维军, 庾灿斌, 徐中岳. 多约束的多阶段积极投资组合模型及实证研究[J]. 运筹学学报, 2018, 22(4): 57-68.
[2]	石礼堂, 陈伟. 非线性无约束优化问题的滤子填充函数算法[J]. 运筹学学报, 2017, 21(1): 55-64.