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Optimal double stopping time

Author

Listed:
  • Magdalena Kobylanski

    (LAMA)

  • Marie-Claire Quenez

    (PMA)

  • Elisabeth Rouy-Mironescu

    (ICJ)

Abstract

We consider the optimal double stopping time problem defined for each stopping time $S$ by $v(S)=\esssup\{E[\psi(\tau_1, \tau_2) | \F_S], \tau_1, \tau_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of a {\em new reward} $\phi$ such that the value function $v(S)$ satisfies $v(S)=\esssup\{E[\phi(\tau) | \F_S], \tau \geq S \}$. Finally, we give an example of an american option with double exercise time.

Suggested Citation

  • Magdalena Kobylanski & Marie-Claire Quenez & Elisabeth Rouy-Mironescu, 2009. "Optimal double stopping time," Papers 0909.3363, arXiv.org.
    • Handle: RePEc:arx:papers:0909.3363
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    File URL: http://arxiv.org/pdf/0909.3363
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