Equilibrium Mean-Variance Dividend Rate Strategies
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915448151343104 |
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| author | Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin |
| author_facet | Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin |
| contents | This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company's dividend strategy, and these features lead to a novel time-inconsistent control problem. To address the time inconsistency, we seek a time-consistent equilibrium dividend rate strategy. We first develop and prove a new verification lemma that characterizes the value function and equilibrium strategy by an extended Hamilton-Jacobi-Bellman system. Next, we apply the verification lemma to obtain the equilibrium strategy and show that it is a barrier strategy for small levels of risk aversion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilibrium Mean-Variance Dividend Rate Strategies Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin Optimization and Control Mathematical Finance 93E20, 91G50, 91B30, 91G05 This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company's dividend strategy, and these features lead to a novel time-inconsistent control problem. To address the time inconsistency, we seek a time-consistent equilibrium dividend rate strategy. We first develop and prove a new verification lemma that characterizes the value function and equilibrium strategy by an extended Hamilton-Jacobi-Bellman system. Next, we apply the verification lemma to obtain the equilibrium strategy and show that it is a barrier strategy for small levels of risk aversion. |
| title | Equilibrium Mean-Variance Dividend Rate Strategies |
| topic | Optimization and Control Mathematical Finance 93E20, 91G50, 91B30, 91G05 |
| url | https://arxiv.org/abs/2508.12047 |