基于半绝对偏差的全部贷款组合区间优化模型

管理评论 ›› 2021, Vol. 33 ›› Issue (2): 15-30.

基于半绝对偏差的全部贷款组合区间优化模型

迟国泰, 李云焕

大连理工大学经济管理学院, 大连 116024

收稿日期:2018-02-23 出版日期:2021-02-28 发布日期:2021-03-08
通讯作者: 迟国泰(通讯作者),大连理工大学经济管理学院教授,博士生导师,博士
作者简介:李云焕,大连理工大学经济管理学院硕士研究生。
基金资助:
国家自然科学基金项目（71731003；71431002；71873103）；国家社会科学基金一般项目（16BTJ017）；国家自然科学基金青年项目（71601041；71503199）。

Loan Portfolio Interval Optimization Model Based on Semi-absolute Deviation

Chi Guotai, Li Yunhuan

School of Economics and Management, Dalian University of Technology, Dalian 116024

Received:2018-02-23 Online:2021-02-28 Published:2021-03-08

摘要/Abstract

摘要： 我国商业银行的利润主要来源于贷款业务，贷款配置的合理与否对银行经营业绩有着直接的影响。本文通过以区间数表示的贷款组合风险最小为目标函数，以区间数表示的目标收益率满足水平为约束条件，建立区间规划模型，对包括存量和增量在内的全部贷款组合的风险进行约束，求解贷款的最优配置。本文的创新与特色：一是基于组合半绝对偏差风险函数来描述组合的风险区间，考虑了多笔贷款收益率之间的相关性，改变了现有线性区间型算法忽略各笔贷款之间的相关性从而夸大组合风险的弊端。二是以全部贷款组合半绝对偏差区间中点m（σ^total）最小为目标来控制风险的大小，以全部贷款组合半绝对偏差区间的半径w（σ^total）最小为目标来控制风险变动的范围，通过多目标规划来兼控“存量组合+增量组合”的全部贷款风险的大小和变动范围。改变了现有研究忽略控制风险区间范围的不足，完善了现有的区间型规划仅仅立足于增量资产配置、忽略巨额存量风险的弊端。三是基于模糊两阶段算法来求解多目标规划模型，解决了多目标线性加权求法加权系数确定不合理，从而导致无法真正实现对两目标同时控制的问题。

关键词: 存量贷款组合, 增量贷款组合, 半绝对偏差, 非线性区间数, 组合优化模型

Abstract: As a main source of profits in China's commercial banks, loan business has direct impact on the operating performance of banks. In this paper, we first establish a risk semi-absolute deviation risk interval based on the principle of semi-absolute deviation risk function. Then we produce an interval planning model by taking the loan portfolio risk represented by the interval number as the objective function and the target rate of return expressed by the interval number as the constraint. This model controls the risk of all loan portfolios, including “incremental portfolio and old portfolio” and solves the optimal allocation of loans. Through empirical analysis, it is shown that this model is superior to the existing models of the same nature.
The main contribution of this research liesin three aspects. First, we describe the risk range based on the combined semi-absolute deviation risk function, which reflects the essence of risk. We consider the correlation between multiple loans to remedy the drawback of the existing linear interval algorithm which neglects the correlation between various loans to exaggerate the portfolio risk. Second, the size of the risk is controlled by minimizing the midpoint of semi-absolute deviation interval of the total loan portfolio m(σ^total), and the range of the risk is controlled by minimizing the radius of semi-absolute deviation interval of the total portfolio w(σ^total), and the multi-objective planning model is established to control the size and scope of the total loan risk including “incremental portfolio and old portfolio”. This model solves the problem of the existing interval planning models which ignore controlling the range of risk interval and altering traditional idea that only considers the risk of incremental portfolio and ignore the huge risk of old portfolio. The third is to solve the multi-objective programming model based on fuzzy two-stage algorithm, which solves the problem of uncertain combinatorial coefficient in multi-objective linear weighting.

Key words: old portfolio, incremental loan portfolio, semi-absolute deviation, nonlinear interval number, portfolio optimal model

迟国泰, 李云焕. 基于半绝对偏差的全部贷款组合区间优化模型[J]. 管理评论, 2021, 33(2): 15-30.

Chi Guotai, Li Yunhuan. Loan Portfolio Interval Optimization Model Based on Semi-absolute Deviation[J]. Management Review, 2021, 33(2): 15-30.

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