Asset-liability management under uncertain economic environment

Dongxu Zhao; Waichon Lio; Fuzhe Huang

doi:10.3934/jimo.2025020

Article Contents

2025, Volume 21, Issue 5: 3486-3499. Doi: 10.3934/jimo.2025020

This issue Previous Article Clean coal technology investment strategy in the coal-electricity supply chain under the cap-and-trade mechanism Next Article Modeling the resilient supplier selection and optimal order Allocation considering the vehicle routing and disruption risk assessment based on the Bayesian network

Asset-liability management under uncertain economic environment

1.
School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
3.
School of Economics, Nankai University, Tianjin 300071, China

^*Corresponding author: Fuzhe Huang
^*Corresponding author: Fuzhe Huang

Received: October 2024

Revised: December 2024

Early access: January 2025

Published: May 2025

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Abstract

This paper addresses an asset-liability management (ALM) framework for uncertain economic environments. By leveraging uncertainty theory and employing continuous-time uncertain differential equations driven by the Liu process to model asset and liability processes, we devise an optimal ALM strategy that achieves a balance between risky and risk-free investments. This strategy is formulated as an uncertain optimal control problem and solved analytically, yielding a closed-form solution. Our sensitivity analysis reveals that higher discount rates, interest rates, and stock appreciation rates encourage more risk-averse strategies, while higher liability appreciation rates lead to increased risk-taking under certain conditions. Additionally, greater risk aversion results in a preference for safer, low-risk investments, while lower risk aversion pushes companies toward more aggressive, high-risk assets.

Keywords:

Mathematics Subject Classification: Primary: 90C70, 90B50; Secondary: 91G05.

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Figure 1. Sensitivity of $ \pi^* $ and $ J $ to Discount Rate $ \delta $

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Figure 2. Sensitivity of $ \pi^* $ and $ J $ to Risk-free rate $ r $

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Figure 3. Sensitivity of $ \pi^* $ and $ J $ to Stock Appreciation Rate $ \mu $

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Figure 4. Sensitivity of $ \pi^* $ and $ J $ to Liability Appreciation Rate $ \beta $

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Figure 5. Sensitivity of $ \pi^* $ and $ J $ to Risk aversion $ \gamma $

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