Value-at-risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model

IF 4.4 3区管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Annals of Operations Research Pub Date : 2025-01-31 DOI:10.1007/s10479-024-06390-x

Marcos Escobar-Anel, Yevhen Havrylenko, Rudi Zagst

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Abstract

We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic programming approach. We demonstrate that the value function in the constrained problem can be represented as the expected modified utility function of a vega-neutral financial derivative on the optimal terminal wealth in the unconstrained utility-maximization problem. Via the same financial derivative, the optimal wealth and the optimal investment strategy in the constrained problem are linked to the optimal wealth and the optimal investment strategy in the unconstrained problem. In numerical studies, we substantiate the impact of risk aversion levels and investment horizons on the optimal investment strategy. We observe a \(20\%\) relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting.

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不完全市场中风险价值约束的投资组合：赫斯顿模型的动态规划方法

在随机波动的不完全金融市场中，我们解决了一个具有风险价值约束的终端投资组合价值的期望效用最大化问题。为了得到最优投资策略，我们使用了动态规划方法。证明了约束问题中的价值函数可以表示为无约束效用最大化问题中对最优终端财富的零中性金融衍生品的期望修正效用函数。通过同一金融导数，将约束问题中的最优财富和最优投资策略与无约束问题中的最优财富和最优投资策略联系起来。在数值研究中，我们证实了风险规避水平和投资期限对最优投资策略的影响。我们观察到，在低风险厌恶的短期环境下，平均参数的约束配置和无约束配置之间存在\(20\%\)的相对差异。

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来源期刊

Annals of Operations Research 管理科学-运筹学与管理科学

CiteScore

7.90

自引率

16.70%

发文量

596

审稿时长

8.4 months

期刊介绍： The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.