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Volume 12
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Article

Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity

by
Dan Zhu
1,
Cuixia Chen
2,* and
Bing Liu
3
1
School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China
2
School of Insurance and Public Finance, Hebei Finance University, Baoding 071051, China
3
School of Finance, Nanjing University of Finance and Economics, Nanjing 210023, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(1), 40; https://doi.org/10.3390/math12010040
Submission received: 14 November 2023 / Revised: 11 December 2023 / Accepted: 13 December 2023 / Published: 22 December 2023
(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)
Versions Notes

Abstract

This study considers the optimal debt ratio and dividend payment policies for an insurer concerned about model misspecification. We assume that the insurer can invest all of its asset to the financial market and the ambiguity may exist in the risky asset. Taking into account the ambiguous situation, the insurer aims to maximize the expected utility of a discounted dividend payment until it ruins. Under some assumption, we prove that there exists classical solutions of the optimal debt ratio, dividend payment policies, and value functions that show that the existence of ambiguity can affect the optimal debt ratio and dividend policies significantly.
Keywords: dividend payment; model ambiguity; optimal debt ratio dividend payment; model ambiguity; optimal debt ratio

Share and Cite

MDPI and ACS Style

Zhu, D.; Chen, C.; Liu, B. Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity. Mathematics 2024, 12, 40. https://doi.org/10.3390/math12010040

AMA Style

Zhu D, Chen C, Liu B. Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity. Mathematics. 2024; 12(1):40. https://doi.org/10.3390/math12010040

Chicago/Turabian Style

Zhu, Dan, Cuixia Chen, and Bing Liu. 2024. "Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity" Mathematics 12, no. 1: 40. https://doi.org/10.3390/math12010040

APA Style

Zhu, D., Chen, C., & Liu, B. (2024). Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity. Mathematics, 12(1), 40. https://doi.org/10.3390/math12010040

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