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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.13302 |
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| _version_ | 1866910137996804096 |
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| author | Mastromonaco, Tommy Fendri, Nacer Renaud, Jean-François Simard, Clarence |
| author_facet | Mastromonaco, Tommy Fendri, Nacer Renaud, Jean-François Simard, Clarence |
| contents | We revisit the optimization problem solved in Løkka & Zervos (2008), i.e., the maximization of dividends, in a Brownian risk model, with the possibility (not the obligation) of making capital injections. Following the approach introduced in Alvarez & Shepp (1998), Renaud & Simard (2021), Renaud et al. (2023), we consider instead absolutely continuous (AC) dividend strategies with an affine bound on the payment rates, while singular capital injections are still allowed. In addition, we incorporate a parameter for the cost of ruin or, said differently, a penalty at ruin in the performance function. We show that the solution is a so-called Løkka-Zervos dichotomy: the surplus is never ruined by making bail-out payments, or no capital is injected and bankruptcy can occur; in either case, dividends are paid at full rate when the surplus is above a threshold. Our framework allows us to provide explicit conditions to express the dichotomy, either using the cost of capital injections or the cost of ruin as a criterion, which also exposes the underlying structure of the solution. In particular, for some values of the parameters, we show that it is optimal to liquidate. Moreover, we perform a numerical analysis highlighting the range of values generated under this AC affine-bound structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13302 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A simple approach to the Løkka-Zervos dichotomy for absolutely continuous dividend strategies Mastromonaco, Tommy Fendri, Nacer Renaud, Jean-François Simard, Clarence Optimization and Control Probability 93E20, 91G05 We revisit the optimization problem solved in Løkka & Zervos (2008), i.e., the maximization of dividends, in a Brownian risk model, with the possibility (not the obligation) of making capital injections. Following the approach introduced in Alvarez & Shepp (1998), Renaud & Simard (2021), Renaud et al. (2023), we consider instead absolutely continuous (AC) dividend strategies with an affine bound on the payment rates, while singular capital injections are still allowed. In addition, we incorporate a parameter for the cost of ruin or, said differently, a penalty at ruin in the performance function. We show that the solution is a so-called Løkka-Zervos dichotomy: the surplus is never ruined by making bail-out payments, or no capital is injected and bankruptcy can occur; in either case, dividends are paid at full rate when the surplus is above a threshold. Our framework allows us to provide explicit conditions to express the dichotomy, either using the cost of capital injections or the cost of ruin as a criterion, which also exposes the underlying structure of the solution. In particular, for some values of the parameters, we show that it is optimal to liquidate. Moreover, we perform a numerical analysis highlighting the range of values generated under this AC affine-bound structure. |
| title | A simple approach to the Løkka-Zervos dichotomy for absolutely continuous dividend strategies |
| topic | Optimization and Control Probability 93E20, 91G05 |
| url | https://arxiv.org/abs/2604.13302 |