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
Pages (from-to)811-833
Number of pages23
JournalScandinavian Actuarial Journal
Issue number8
Early online dateMar 2023
Publication statusPublished - 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


Dive into the research topics of 'Time-inconsistent view on a dividend problem with penalty'. Together they form a unique fingerprint.

Cite this