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- W2950895197 abstract "Let $X$ be a one-dimensional diffusion and let $gcolon[0,T]timesmathbb{R}tomathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function $pi:[0,T]tomathbb{R}$ such that a given stopping time $tau^{star}$ is a solution of the stopping problem $sup_{tau}mathbb{E}left[g(tau,X_{tau})+pi(tau)right],.$ Under regularity and monotonicity conditions, there exists a solution $pi$ if and only if $tau^{star}$ is the first time when $X$ exceeds a time-dependent barrier $b$, i.e. $tau^{star}=infleft{ tge0,|,X_{t}ge b(t)right} ,.$ We prove uniqueness of the solution $pi$ and derive a closed form representation. The representation is based on an auxiliary process which is a version of the original diffusion $X$ reflected at $b$ towards the continuation region. The results lead to a new integral equation characterizing the stopping boundary $b$ of the stopping problem $sup_{tau}mathbb{E}left[g(tau,X_{tau})right]$." @default.
- W2950895197 created "2019-06-27" @default.
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- W2950895197 date "2014-06-01" @default.
- W2950895197 modified "2023-09-27" @default.
- W2950895197 title "An inverse optimal stopping problem for diffusion processes" @default.
- W2950895197 hasPublicationYear "2014" @default.
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