Optimal Dividends and Proactive Capital Injection over a Finite Horizon
Abstract
We study a finite-horizon dividend and capital-injection problem for a Brownian surplus process with time-varying financing costs. Under a classical passive-injection policy, capital is supplied only at the solvency boundary. Anticipated increases in financing costs may instead make it optimal to inject capital while reserves remain strictly positive. We characterize this proactive financing mechanism through an auxiliary Dynkin game for the marginal value of liquidity. The game identifies an endogenous lower financing boundary and an upper dividend boundary, and yields restrictions on intervention timing and comparative statics with respect to the financing-cost path. Under a regular intervention-band condition, we recover the control value by spatial integration of the game value and verify that the optimal policy is two-sided reflection between the two boundaries. We establish this condition for a canonical class with decreasing marginal dividend rewards, increasing marginal financing costs, and a compatible piecewise affine terminal marginal value. Strictly decreasing financing costs eliminate positive-reserve financing contact and reduce the marginal game to a one-player stopping problem. Numerical examples illustrate the optimal policies and the effects of anticipated financing conditions on shareholder value and intervention thresholds.
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BibTeX
@misc{xu2026optimal,
title = {{Optimal Dividends and Proactive Capital Injection over a Finite Horizon}},
author = {Ran Xu and Zuo Quan Xu and Xueying Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29085},
eprint = {2610.29085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29085},
}
RIS
TY - UNPB
TI - Optimal Dividends and Proactive Capital Injection over a Finite Horizon
AU - Ran Xu
AU - Zuo Quan Xu
AU - Xueying Zhang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29085
UR - https://arxiv.org/abs/2610.29085
AB - We study a finite-horizon dividend and capital-injection problem for a Brownian surplus process with time-varying financing costs. Under a classical passive-injection policy, capital is supplied only at the solvency boundary. Anticipated increases in financing costs may instead make it optimal to inject capital while reserves remain strictly positive. We characterize this proactive financing mechanism through an auxiliary Dynkin game for the marginal value of liquidity. The game identifies an endogenous lower financing boundary and an upper dividend boundary, and yields restrictions on intervention timing and comparative statics with respect to the financing-cost path. Under a regular intervention-band condition, we recover the control value by spatial integration of the game value and verify that the optimal policy is two-sided reflection between the two boundaries. We establish this condition for a canonical class with decreasing marginal dividend rewards, increasing marginal financing costs, and a compatible piecewise affine terminal marginal value. Strictly decreasing financing costs eliminate positive-reserve financing contact and reduce the marginal game to a one-player stopping problem. Numerical examples illustrate the optimal policies and the effects of anticipated financing conditions on shareholder value and intervention thresholds.
ER -