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Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem .
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the odds strategy, and the importance of the odds strategy lies in its optimality, as explained below.
The optimal policy for the problem is a stopping rule. Under it, the interviewer rejects the first r − 1 applicants (let applicant M be the best applicant among these r − 1 applicants), and then selects the first subsequent applicant that is better than applicant M. It can be shown that the optimal strategy lies in this class of strategies.
Another optimal stopping problem bearing Robbins' name is the Chow–Robbins game: [8] [9] Given an infinite sequence of IID random variables ,,... with distribution , how to decide when to stop, in order to maximize the sample average (+) where is the stopping time?
Limited-memory BFGS method — truncated, matrix-free variant of BFGS method suitable for large problems; Steffensen's method — uses divided differences instead of the derivative; Secant method — based on linear interpolation at last two iterates; False position method — secant method with ideas from the bisection method
More recently, in 2011, an extension of the SPRT method called Maximized Sequential Probability Ratio Test (MaxSPRT) [7] was introduced. The salient feature of MaxSPRT is the allowance of a composite, one-sided alternative hypothesis, and the introduction of an upper stopping boundary. The method has been used in several medical research ...
The model is a simple regenerative optimal stopping stochastic ... using Newton–Kantorovich iterations to calculate ... This method is faster to compute than non ...
In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating ...