Time-inconsistent view on a dividend problem with penalty

Josef Anton Strini*, Stefan Thonhauser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example
Original languageEnglish
Number of pages30
JournalScandinavian Actuarial Journal
Early online dateMar 2023
Publication statusE-pub ahead of print - Mar 2023


  • dividends
  • extended Hamilton–Jacobi–Bellman equation
  • Ruin theory
  • time-inconsistent stochastic control

ASJC Scopus subject areas

  • Economics and Econometrics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fields of Expertise

  • Information, Communication & Computing


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