The High Contact Principle in Optimal Stopping and Stochastic Waves

  • Bernt Øksendal
Part of the Progress in Probability book series (PRPR, volume 18)


The high contact principle in optimal stopping states that at the boundary ∂D of the continuation region D the reward function g has a smooth fit with the optimal expected reward function g*, in the sense that
$$\begin{gathered} g = {g^*}on{\text{ }}\partial D \hfill \\ \nabla g = \nabla g*on{\text{ }}\partial D \hfill \\ \end{gathered} $$
Thus this principle gives the crucial link between optimal stopping and free boundary problems.


Variational Inequality Stochastic Differential Equation Free Boundary Problem Reward Function Geometric Brownian Motion 
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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Bernt Øksendal
    • 1
  1. 1.Dept. of MathematicsUniversity of California, San DiegoLa JollaUSA

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