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- W2017113237 abstract "Let $Y_t$ be a stochastic process starting at $y$ which changes by i.i.d. dichotomous increments $X_t$ with mean 0 and variance 1. The cost of proceeding one step is one and the payoff is zero unless $n$ steps are taken and the final value $hat{Y}$ of $Y_t$ is negative in which case the payoff is $hat{Y}^2$. The optimal procedure consists of stopping as soon as $Y_t geq tilde{y}_m$ where $m$ is the number of steps left to be taken. The limit of $tilde{y}_m$ as $m rightarrow infty$ is desired as a function of $p = P(X_t < 0)$. This limit $tilde{y}$ is evaluated for $p$ rational and proved to be continuous in $p$. One can use $tilde{y}$ to relate the solution of optimal stopping problems involving a Wiener process to those involving certain discrete-time discrete-process stopping problems. Thus $tilde{y}$ is useful in calculating simple numerical approximations to solutions of various stopping problems." @default.
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- W2017113237 date "1976-12-01" @default.
- W2017113237 modified "2023-09-24" @default.
- W2017113237 title "An Optimal Stopping Problem for Sums of Dichotomous Random Variables" @default.
- W2017113237 doi "https://doi.org/10.1214/aop/1176995933" @default.
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