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Maximization of the Survival Probability by Franchise and Deductible Amounts in the Classical Risk Model

In: Modern Stochastics and Applications

Author

Listed:
  • Olena Ragulina

    (Donetsk National University)

Abstract

We consider the classical risk model when an insurance company has the opportunity to adjust franchise amount continuously. The problem of optimal control by franchise amount is solved from viewpoint of survival probability maximization. We derive the Hamilton–Jacobi–Bellman equation for the optimal survival probability and prove the existence of a solution of this equation with certain properties. The verification theorem gives the connection between this solution and the optimal survival probability. Then we concentrate on the case of exponentially distributed claim sizes. Finally, we extend the obtained results to the problem of optimal control by deductible amount.

Suggested Citation

  • Olena Ragulina, 2014. "Maximization of the Survival Probability by Franchise and Deductible Amounts in the Classical Risk Model," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 287-300, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-03512-3_16
    DOI: 10.1007/978-3-319-03512-3_16
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