Optimal dividend payment under a ruin constraint: Discrete time and state space

Optimale Dividendenzahlung unter einer Ruin-Nebenbedingung im diskreten Zustandsraum und bei diskreter Zeit

Summary

We consider optimal dividend payment under the constraint that the controlled risk process has a ruin probability which does not exceed a given bound. The underlying simple model has independent identically distributed total claims per year and a constant yearly premium, all integers. The solution to this constraint optimization problem is given in a modified Hamilton-Jacobi-Bellman (HJB) equation. It is shown that this equation has a solution, and a verification argument is given showing that the solution of the HJB equation is the value function of the optimization problem. The optimal dividend payment strategy is given in the usual feedback form.

Zusammenfassung

Optimale Dividendenzahlung wird berechnet unter der Nebenbedingung, dass der so kontrollierte Reserveprozess eine vorgegebene Ruinwahrscheinlichkeit nicht überschreitet. Das zugrundeliegende einfache Modell hat unabhängige identisch verteilte ganzzahlige Gesamtschäden pro Jahr und eine ebenfalls ganzzahlige konstante Jahresprämie. Die Lösung wird in der Form einer modifizierten Hamilton-Jacobi-Bellman Gleichung angegeben, für die die Existenz einer Lösung und das Verifikationslemma nachgewiesen wird.

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Correspondence to Christian Hipp.

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Hipp, C. Optimal dividend payment under a ruin constraint: Discrete time and state space. Blätter DGVFM 26, 255–264 (2003). https://doi.org/10.1007/BF02808376

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Keywords

  • Risk Process
  • Dividend Payment
  • Dividend Payout
  • Claim Size
  • Optimal Dividend