Dislocation dynamics and Optimal stopping problem: Difference between pages
(Difference between pages)
imported>Nestor (Created page with "Dislocations are microscopic defects in crystals that change over time (due for instance to shear stresses on the crystal). If we have a finite number of parallel (horizontal) ...") |
imported>Luis (Created page with "This is an excerpt from the main article on the optimal stopping problem. Given a Levy process $X_t$ we consider the following problem. We want to find the optimal stopp...") |
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This is an excerpt from the main article on the [[optimal stopping problem]]. | |||
Given a [[Levy process]] $X_t$ we consider the following problem. We want to find the optimal stopping time $\tau$ to maximize the expected value of $\varphi(X_{\tau})$ for some given (payoff) function $\varphi$. | |||
\ | In this setting, the value of $\varphi(X_{\tau})$ depends on the initial point $x$ where the Levy process starts. We can call $u(x) = \mathbb E[\varphi(X_{\tau}) | X_0 = x]$. Under this choice, the function $u$ satisfies the obstacle problem with $L$ being the generator of the Levy process $X_t$. | ||
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Revision as of 13:52, 28 January 2012
This is an excerpt from the main article on the optimal stopping problem.
Given a Levy process $X_t$ we consider the following problem. We want to find the optimal stopping time $\tau$ to maximize the expected value of $\varphi(X_{\tau})$ for some given (payoff) function $\varphi$.
In this setting, the value of $\varphi(X_{\tau})$ depends on the initial point $x$ where the Levy process starts. We can call $u(x) = \mathbb E[\varphi(X_{\tau}) | X_0 = x]$. Under this choice, the function $u$ satisfies the obstacle problem with $L$ being the generator of the Levy process $X_t$.