On the best order of observation in optimal stopping problems

1987 ◽  
Vol 24 (3) ◽  
pp. 773-778 ◽  
Author(s):  
David Gilat
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Similar Nature ◽  
Optimal Stopping Problems

For optimal stopping problems in which the player is allowed to choose the order of the random variables as well as the stopping rule, a notion of order equivalence is introduced. It is shown that different (non-degenerate) distributions cannot be order-equivalent.This result unifies and generalizes two theorems of a similar nature recently obtained by Hill and Hordijk (1985).

On the best order of observation in optimal stopping problems

1987 ◽  
Vol 24 (03) ◽  
pp. 773-778 ◽  
Author(s):  
David Gilat
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Similar Nature ◽  
Optimal Stopping Problems

For optimal stopping problems in which the player is allowed to choose the order of the random variables as well as the stopping rule, a notion of order equivalence is introduced. It is shown that different (non-degenerate) distributions cannot be order-equivalent. This result unifies and generalizes two theorems of a similar nature recently obtained by Hill and Hordijk (1985).

Selection of order of observation in optimal stopping problems

1985 ◽  
Vol 22 (1) ◽  
pp. 177-184 ◽  
Author(s):  
Theodore P. Hill ◽  
Arie Hordijk
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
The Other ◽  
Other Hand ◽  
General Rules ◽  
Optimal Stopping Problems ◽  
Optimal Ordering ◽  
Uniformly Bounded ◽  
Selection Of

In optimal stopping problems in which the player is free to choose the order of observation of the random variables as well as the stopping rule, it is shown that in general there is no function of all the moments of individual integrable random variables, nor any function of the first n moments of uniformly bounded random variables, which can determine the optimal ordering. On the other hand, several fairly general rules for identification of the optimal ordering based on individual distributions are given, and applications are made to several special classes of distributions.

Selection of order of observation in optimal stopping problems

1985 ◽  
Vol 22 (01) ◽  
pp. 177-184 ◽  
Author(s):  
Theodore P. Hill ◽  
Arie Hordijk
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
The Other ◽  
Other Hand ◽  
General Rules ◽  
Optimal Stopping Problems ◽  
Optimal Ordering ◽  
Uniformly Bounded ◽  
Selection Of

In optimal stopping problems in which the player is free to choose the order of observation of the random variables as well as the stopping rule, it is shown that in general there is no function of all the moments of individual integrable random variables, nor any function of the first n moments of uniformly bounded random variables, which can determine the optimal ordering. On the other hand, several fairly general rules for identification of the optimal ordering based on individual distributions are given, and applications are made to several special classes of distributions.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (02) ◽  
pp. 241-266
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (2) ◽  
pp. 241-266 ◽  
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

Optimal stopping problems with generalized objective functions

1990 ◽  
Vol 27 (04) ◽  
pp. 828-838
Author(s):  
T. P. Hill ◽  
D. P. Kennedy
Keyword(s):  
Optimal Stopping ◽  
Stopping Time ◽  
Random Variables ◽  
Stopping Times ◽  
Objective Functions ◽  
Monotone Functions ◽  
Optimal Stopping Problems ◽  
Universal Bounds ◽  
Optimal Stopping Times ◽  
Entire Vector

Optimal stopping of a sequence of random variables is studied, with emphasis on generalized objectives which may be non-monotone functions ofEXt, wheretis a stopping time, or may even depend on the entire vector (E[X1I{t=l}], · ··,E[XnI{t=n}]),such as the minimax objective to maximize minj{E[XjI{t=j}]}.Convexity is used to establish a prophet inequality and universal bounds for the optimal return, and a method for constructing optimal stopping times for such objectives is given.

scholarly journals An optimal sequential procedure for a buying-selling problem with independent observations

2006 ◽  
Vol 43 (02) ◽  
pp. 454-462 ◽  
Author(s):  
G. Sofronov ◽  
Jonathan M. Keith ◽  
Dirk P. Kroese
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Sequential Procedure ◽  
Independent Random Variables ◽  
Value Of A Game ◽  
Optimal Stopping Rule ◽  
Independent Observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

scholarly journals An optimal sequential procedure for a buying-selling problem with independent observations

2006 ◽  
Vol 43 (2) ◽  
pp. 454-462 ◽  
Author(s):  
G. Sofronov ◽  
Jonathan M. Keith ◽  
Dirk P. Kroese
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Sequential Procedure ◽  
Independent Random Variables ◽  
Value Of A Game ◽  
Optimal Stopping Rule ◽  
Independent Observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

Optimal stopping problems with generalized objective functions

1990 ◽  
Vol 27 (4) ◽  
pp. 828-838
Author(s):  
T. P. Hill ◽  
D. P. Kennedy
Keyword(s):  
Optimal Stopping ◽  
Stopping Time ◽  
Random Variables ◽  
Stopping Times ◽  
Objective Functions ◽  
Monotone Functions ◽  
Optimal Stopping Problems ◽  
Universal Bounds ◽  
Optimal Stopping Times ◽  
Entire Vector

Optimal stopping of a sequence of random variables is studied, with emphasis on generalized objectives which may be non-monotone functions of EXt, where t is a stopping time, or may even depend on the entire vector (E[X1I{t=l}], · ··, E[XnI{t=n}]), such as the minimax objective to maximize minj{E[XjI{t=j}]}. Convexity is used to establish a prophet inequality and universal bounds for the optimal return, and a method for constructing optimal stopping times for such objectives is given.

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