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arXiv · 2604.13302

A new perspective on the L{\o}kka-Zervos dichotomy for absolutely continuous dividend strategies

Tommy Mastromonaco·Nacer Fendri·Jean-François Renaud·Clarence Simard
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Abstract

We revisit the optimization problem (and its dichotomous solution) analyzed in Renaud et al. (2026). By choosing affine functions (of the surplus level) to bound the dividend rates, we are able to provide a more explicit derivation of the solution, avoiding the use of viscosity solutions. Moreover, with explicitly parameterized expressions, we are able to study analytical properties of the optimal thresholds and to refine the statement of the dichotomy. To reach these objectives, we add a penalty-at-ruin parameter in the performance function, allowing us to unify the expressions of the value functions of the two subproblems appearing in the dichotomous solution; as a by-product, the dichotomy can also be expressed in terms of this newly added parameter. Finally, we perform sensitivity analyses to illustrate that the range of values generated in an affine-bound framework is flexible and can span the range from a constant bound to the singular version of this problem.

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Tommy Mastromonaco, Nacer Fendri, Jean-François Renaud, Clarence Simard. 2026-04-14. A new perspective on the L{\o}kka-Zervos dichotomy for absolutely continuous dividend strategies. https://arxiv.org/abs/2604.13302

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