Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints

IF 1 2区数学 Q3 STATISTICS & PROBABILITY

Probability Uncertainty and Quantitative Risk Pub Date : 2021-11-17 DOI:10.3934/puqr.2023012

Zixin Feng, D. Tian

引用次数: 0

Abstract

The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation (BSDE). Due to the stochastic market environment, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. After establishing the martingale optimality criterion, by delicately selecting Lyapunov functions, the verification theorem is ultimately obtained. Besides, several examples and numerical simulations for the optimal strategies are provided and illustrated.

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一般约束下具有Epstein-Zin效用的最优消费与投资组合选择

研究了不完全市场中具有Epstein-Zin效用的投资者的消费-投资问题。封闭的(不一定是凸的)约束强加于策略。通过二次倒向随机微分方程(BSDE)描述了最优消费和投资策略。由于市场环境是随机的，这个BSDE的解是无界的，因此BMO的论点就站不住脚了。在建立鞅最优性准则后，通过对李雅普诺夫函数的精细选择，最终得到验证定理。此外，还给出了若干优化策略的算例和数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Probability Uncertainty and Quantitative Risk STATISTICS & PROBABILITY-

CiteScore

1.60

自引率

13.30%

发文量

审稿时长

12 weeks

期刊介绍： Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1). Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.