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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.
Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory.
In probability theory, Robbins' problem of optimal stopping [1], named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. [2] Let X 1, ... , X n be independent, identically distributed random variables, uniform on [0, 1].
In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function, which are solutions to the equation =. However, to optimize a twice-differentiable f {\displaystyle f} , our goal is to find the roots of f ′ {\displaystyle f'} .
Optimal stopping — choosing the optimal time to take a particular action Odds algorithm; Robbins' problem; Global optimization: BRST algorithm; MCS algorithm; Multi-objective optimization — there are multiple conflicting objectives Benson's algorithm — for linear vector optimization problems
The "index policy" induced by the Gittins index, consisting of choosing at any time the stochastic process with the currently highest Gittins index, is the solution of some stopping problems such as the one of dynamic allocation, where a decision-maker has to maximize the total reward by distributing a limited amount of effort to a number of ...
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. [1]