Log in

Relevant bibliographies by topics / Optimal stopping rules / Journal articles

Journal articles on the topic 'Optimal stopping rules'

To see the other types of publications on this topic, follow the link: Optimal stopping rules.

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Optimal stopping rules.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Assaf, David, and Ester Samuel-Cahn. "Optimal multivariate stopping rules." Journal of Applied Probability 35, no. 3 (September 1998): 693–706. http://dx.doi.org/10.1239/jap/1032265217.

Full text

Abstract:

For fixed i let X(i) = (X1(i), …, Xd(i)) be a d-dimensional random vector with some known joint distribution. Here i should be considered a time variable. Let X(i), i = 1, …, n be a sequence of n independent vectors, where n is the total horizon. In many examples Xj(i) can be thought of as the return to partner j, when there are d ≥ 2 partners, and one stops with the ith observation. If the jth partner alone could decide on a (random) stopping rule t, his goal would be to maximize EXj(t) over all possible stopping rules t ≤ n. In the present ‘multivariate’ setup the d partners must however cooperate and stop at the same stopping time t, so as to maximize some agreed function h(∙) of the individual expected returns. The goal is thus to find a stopping rule t* for which h(EX1 (t), …, EXd(t)) = h (EX(t)) is maximized. For continuous and monotone h we describe the class of optimal stopping rules t*. With some additional symmetry assumptions we show that the optimal rule is one which (also) maximizes EZt where Zi = ∑dj=1Xj(i), and hence has a particularly simple structure. Examples are included, and the results are extended both to the infinite horizon case and to the case when X(1), …, X(n) are dependent. Asymptotic comparisons between the present problem of finding suph(EX(t)) and the ‘classical’ problem of finding supEh(X(t)) are given. Comparisons between the optimal return to the statistician and to a ‘prophet’ are also included. In the present context a ‘prophet’ is someone who can base his (random) choice g on the full sequence X(1), …, X(n), with corresponding return suph(EX(g)).

APA, Harvard, Vancouver, ISO, and other styles

2

Assaf, David, and Ester Samuel-Cahn. "Optimal multivariate stopping rules." Journal of Applied Probability 35, no. 03 (September 1998): 693–706. http://dx.doi.org/10.1017/s002190020001634x.

Full text

Abstract:

For fixediletX(i) = (X1(i), …,Xd(i)) be ad-dimensional random vector with some known joint distribution. Hereishould be considered a time variable. LetX(i),i= 1, …,nbe a sequence ofnindependent vectors, wherenis the total horizon. In many examplesXj(i) can be thought of as the return to partnerj, when there ared≥ 2 partners, and one stops with theith observation. If thejth partner alone could decide on a (random) stopping rulet, his goal would be to maximizeEXj(t) over all possible stopping rulest≤n. In the present ‘multivariate’ setup thedpartners must however cooperate and stop at thesamestopping timet, so as to maximize some agreed functionh(∙) of the individual expected returns. The goal is thus to find a stopping rulet*for whichh(EX1(t), …,EXd(t)) =h(EX(t)) is maximized. For continuous and monotonehwe describe the class of optimal stopping rulest*. With some additional symmetry assumptions we show that the optimal rule is one which (also) maximizesEZtwhereZi= ∑dj=1Xj(i), and hence has a particularly simple structure. Examples are included, and the results are extended both to the infinite horizon case and to the case whenX(1), …,X(n) are dependent. Asymptotic comparisons between the present problem of finding suph(EX(t)) and the ‘classical’ problem of finding supEh(X(t)) are given. Comparisons between the optimal return to the statistician and to a ‘prophet’ are also included. In the present context a ‘prophet’ is someone who can base his (random) choicegon the full sequenceX(1), …,X(n), with corresponding return suph(EX(g)).

APA, Harvard, Vancouver, ISO, and other styles

3

Karni, Edi, and Zvi Safra. "Behaviorally consistent optimal stopping rules." Journal of Economic Theory 51, no. 2 (August 1990): 391–402. http://dx.doi.org/10.1016/0022-0531(90)90024-e.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Ferguson, T. S., and J. P. Hardwick. "Stopping rules for proofreading." Journal of Applied Probability 26, no. 02 (June 1989): 304–13. http://dx.doi.org/10.1017/s0021900200027303.

Full text

Abstract:

A manuscript with an unknown random numberMof misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On thenthproofreading, each remaining misprint is detected independently with probabilitypn– 1. Each proofreading costs an amountCP> 0, and if one stops afternproofreadings, each misprint overlooked costs an amountcn> 0. Two models are treated based on the distribution ofM.In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.

APA, Harvard, Vancouver, ISO, and other styles

5

Ferguson, T. S., and J. P. Hardwick. "Stopping rules for proofreading." Journal of Applied Probability 26, no. 2 (June 1989): 304–13. http://dx.doi.org/10.2307/3214037.

Full text

Abstract:

A manuscript with an unknown random number M of misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On the nthproofreading, each remaining misprint is detected independently with probability pn– 1. Each proofreading costs an amount CP > 0, and if one stops after n proofreadings, each misprint overlooked costs an amount cn > 0. Two models are treated based on the distribution of M. In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.

APA, Harvard, Vancouver, ISO, and other styles

6

Ankirchner, Stefan, and Maike Klein. "Bayesian sequential testing with expectation constraints." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 51. http://dx.doi.org/10.1051/cocv/2019045.

Full text

Abstract:

We study a stopping problem arising from a sequential testing of two simple hypotheses H0 and H1 on the drift rate of a Brownian motion. We impose an expectation constraint on the stopping rules allowed and show that an optimal stopping rule satisfying the constraint can be found among the rules of the following type: stop if the posterior probability for H1 attains a given lower or upper barrier; or stop if the posterior probability comes back to a fixed intermediate point after a sufficiently large excursion. Stopping at the intermediate point means that the testing is abandoned without accepting H0 or H1. In contrast to the unconstrained case, optimal stopping rules, in general, cannot be found among interval exit times. Thus, optimal stopping rules in the constrained case qualitatively differ from optimal rules in the unconstrained case.

APA, Harvard, Vancouver, ISO, and other styles

7

Chow, Chung-Wen, and Zvi Schechner. "On stopping rules in proofreading." Journal of Applied Probability 22, no. 4 (December 1985): 971–77. http://dx.doi.org/10.2307/3213967.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Chow, Chung-Wen, and Zvi Schechner. "On stopping rules in proofreading." Journal of Applied Probability 22, no. 04 (December 1985): 971–77. http://dx.doi.org/10.1017/s002190020010823x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Allaart, Pieter, and Michael Monticino. "Optimal stopping rules for directionally reinforced processes." Advances in Applied Probability 33, no. 2 (June 2001): 483–504. http://dx.doi.org/10.1017/s0001867800010909.

Full text

Abstract:

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement behavior. Explicit descriptions of optimal stopping rules are given in several interesting special cases with and without transaction costs. Numerical examples are presented comparing optimal strategies to simpler buy and hold strategies.

APA, Harvard, Vancouver, ISO, and other styles

10

Allaart, Pieter, and Michael Monticino. "Optimal stopping rules for directionally reinforced processes." Advances in Applied Probability 33, no. 2 (2001): 483–504. http://dx.doi.org/10.1239/aap/999188325.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Engen, Steinar, and Eva Seim. "Uniformly best invariant stopping rules." Journal of Applied Probability 24, no. 1 (March 1987): 77–87. http://dx.doi.org/10.2307/3214060.

Full text

Abstract:

The class of stopping rules for a sequence of i.i.d. random variables with partially known distribution is restricted by requiring invariance with respect to certain transformations. Invariant stopping rules have an intuitive appeal when the optimal stopping problem is invariant with respect to the actual gain function. Uniformly best invariant stopping rules are derived for the gamma distribution with known shape parameter and unknown scale parameter, for the uniform distribution with both endpoints unknown, and for the normal distribution with unknown mean and variance. Some comparisons with previously published results are made.

APA, Harvard, Vancouver, ISO, and other styles

12

Engen, Steinar, and Eva Seim. "Uniformly best invariant stopping rules." Journal of Applied Probability 24, no. 01 (March 1987): 77–87. http://dx.doi.org/10.1017/s002190020003062x.

Full text

Abstract:

The class of stopping rules for a sequence of i.i.d. random variables with partially known distribution is restricted by requiring invariance with respect to certain transformations. Invariant stopping rules have an intuitive appeal when the optimal stopping problem is invariant with respect to the actual gain function. Uniformly best invariant stopping rules are derived for the gamma distribution with known shape parameter and unknown scale parameter, for the uniform distribution with both endpoints unknown, and for the normal distribution with unknown mean and variance. Some comparisons with previously published results are made.

APA, Harvard, Vancouver, ISO, and other styles

13

Allaart, Pieter. "Optimal stopping rules for correlated random walks with a discount." Journal of Applied Probability 41, no. 2 (June 2004): 483–96. http://dx.doi.org/10.1239/jap/1082999080.

Full text

Abstract:

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

APA, Harvard, Vancouver, ISO, and other styles

14

Allaart, Pieter. "Optimal stopping rules for correlated random walks with a discount." Journal of Applied Probability 41, no. 02 (June 2004): 483–96. http://dx.doi.org/10.1017/s0021900200014443.

Full text

Abstract:

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

APA, Harvard, Vancouver, ISO, and other styles

15

Hobson, David, and Matthew Zeng. "Randomised rules for stopping problems." Journal of Applied Probability 57, no. 3 (September 2020): 981–1004. http://dx.doi.org/10.1017/jpr.2020.43.

Full text

Abstract:

AbstractIn a classical, continuous-time, optimal stopping problem, the agent chooses the best time to stop a stochastic process in order to maximise the expected discounted return. The agent can choose when to stop, and if at any moment they decide to stop, stopping occurs immediately with probability one. However, in many settings this is an idealistic oversimplification. Following Strack and Viefers we consider a modification of the problem in which stopping occurs at a rate which depends on the relative values of stopping and continuing: there are several different solutions depending on how the value of continuing is calculated. Initially we consider the case where stopping opportunities are constrained to be event times of an independent Poisson process. Motivated by the limiting case as the rate of the Poisson process increases to infinity, we also propose a continuous-time formulation of the problem where stopping can occur at any instant.

APA, Harvard, Vancouver, ISO, and other styles

16

Assaf, David, Larry Goldstein, and Ester Samuel-Cahn. "Two-choice optimal stopping." Advances in Applied Probability 36, no. 4 (December 2004): 1116–47. http://dx.doi.org/10.1239/aap/1103662960.

Full text

Abstract:

Let Xn,…,X1 be independent, identically distributed (i.i.d.) random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose Xs using stopping rules. The statistician's goal is to stop at a value of X as small as possible. Let equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behaviour of the sequence for a large class of Fs belonging to the domain of attraction (for the minimum) 𝒟(Gα), where Gα(x) = [1 - exp(-xα)]1(x ≥ 0) (with 1(·) the indicator function). The results are compared with those for the asymptotic behaviour of the classical one-choice value sequence , as well as with the ‘prophet value’ sequence

APA, Harvard, Vancouver, ISO, and other styles

17

Assaf, David, Larry Goldstein, and Ester Samuel-Cahn. "Two-choice optimal stopping." Advances in Applied Probability 36, no. 04 (December 2004): 1116–47. http://dx.doi.org/10.1017/s0001867800013331.

Full text

Abstract:

Let X n ,…,X 1 be independent, identically distributed (i.i.d.) random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose Xs using stopping rules. The statistician's goal is to stop at a value of X as small as possible. Let equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behaviour of the sequence for a large class of Fs belonging to the domain of attraction (for the minimum) 𝒟(G α), where G α(x) = [1 - exp(-x α)]1(x ≥ 0) (with 1(·) the indicator function). The results are compared with those for the asymptotic behaviour of the classical one-choice value sequence , as well as with the ‘prophet value’ sequence

APA, Harvard, Vancouver, ISO, and other styles

18

Helmes, Kurt, and Richard H. Stockbridge. "Construction of the Value Function and Optimal Rules in Optimal Stopping of One-Dimensional Diffusions." Advances in Applied Probability 42, no. 1 (March 2010): 158–82. http://dx.doi.org/10.1239/aap/1269611148.

Full text

Abstract:

A new approach to the solution of optimal stopping problems for one-dimensional diffusions is developed. It arises by imbedding the stochastic problem in a linear programming problem over a space of measures. Optimizing over a smaller class of stopping rules provides a lower bound on the value of the original problem. Then the weak duality of a restricted form of the dual linear program provides an upper bound on the value. An explicit formula for the reward earned using a two-point hitting time stopping rule allows us to prove strong duality between these problems and, therefore, allows us to either optimize over these simpler stopping rules or to solve the restricted dual program. Each optimization problem is parameterized by the initial value of the diffusion and, thus, we are able to construct the value function by solving the family of optimization problems. This methodology requires little regularity of the terminal reward function. When the reward function is smooth, the optimal stopping locations are shown to satisfy the smooth pasting principle. The procedure is illustrated using two examples.

APA, Harvard, Vancouver, ISO, and other styles

19

Helmes, Kurt, and Richard H. Stockbridge. "Construction of the Value Function and Optimal Rules in Optimal Stopping of One-Dimensional Diffusions." Advances in Applied Probability 42, no. 01 (March 2010): 158–82. http://dx.doi.org/10.1017/s0001867800003955.

Full text

Abstract:

A new approach to the solution of optimal stopping problems for one-dimensional diffusions is developed. It arises by imbedding the stochastic problem in a linear programming problem over a space of measures. Optimizing over a smaller class of stopping rules provides a lower bound on the value of the original problem. Then the weak duality of a restricted form of the dual linear program provides an upper bound on the value. An explicit formula for the reward earned using a two-point hitting time stopping rule allows us to prove strong duality between these problems and, therefore, allows us to either optimize over these simpler stopping rules or to solve the restricted dual program. Each optimization problem is parameterized by the initial value of the diffusion and, thus, we are able to construct the value function by solving the family of optimization problems. This methodology requires little regularity of the terminal reward function. When the reward function is smooth, the optimal stopping locations are shown to satisfy the smooth pasting principle. The procedure is illustrated using two examples.

APA, Harvard, Vancouver, ISO, and other styles

20

Roters, Markus. "Optimal Stopping in a Dice Game." Journal of Applied Probability 35, no. 1 (March 1998): 229–35. http://dx.doi.org/10.1239/jap/1032192566.

Full text

Abstract:

In this paper we consider an explicit solution of an optimal stopping problem arising in connection with a dice game. An optimal stopping rule and the maximum expected reward in this problem can easily be computed by means of the distributions involved and the specific rules of the game

APA, Harvard, Vancouver, ISO, and other styles

21

Roters, Markus. "Optimal Stopping in a Dice Game." Journal of Applied Probability 35, no. 01 (March 1998): 229–35. http://dx.doi.org/10.1017/s0021900200014820.

Full text

Abstract:

In this paper we consider an explicit solution of an optimal stopping problem arising in connection with a dice game. An optimal stopping rule and the maximum expected reward in this problem can easily be computed by means of the distributions involved and the specific rules of the game

APA, Harvard, Vancouver, ISO, and other styles

22

Ye, Lu. "Value Function and Optimal Rule on the Optimal Stopping Problem for Continuous-Time Markov Processes." Chinese Journal of Mathematics 2017 (October 9, 2017): 1–10. http://dx.doi.org/10.1155/2017/3596037.

Full text

Abstract:

This paper considers the optimal stopping problem for continuous-time Markov processes. We describe the methodology and solve the optimal stopping problem for a broad class of reward functions. Moreover, we illustrate the outcomes by some typical Markov processes including diffusion and Lévy processes with jumps. For each of the processes, the explicit formula for value function and optimal stopping time is derived. Furthermore, we relate the derived optimal rules to some other optimal problems.

APA, Harvard, Vancouver, ISO, and other styles

23

Dubins, L. E., L. A. Shepp, and A. N. Shiryaev. "Optimal Stopping Rules and Maximal Inequalities for Bessel Processes." Theory of Probability & Its Applications 38, no. 2 (June 1994): 226–61. http://dx.doi.org/10.1137/1138024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Meier, Martin, and Leopold Sögner. "A new strategy for Robbins’ problem of optimal stopping." Journal of Applied Probability 54, no. 1 (March 2017): 331–36. http://dx.doi.org/10.1017/jpr.2016.103.

Full text

Abstract:

AbstractIn this paper we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest nontrivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in particular, we obtain an expected rank of 2.326 14.

APA, Harvard, Vancouver, ISO, and other styles

25

ARTILES-LE[Qacute]N, NOEL, HERBERT T. DAVID, and HOWARD D. MEEKS. "Statistical optimal design of control charts with supplementary stopping rules." IIE Transactions 28, no. 3 (March 1996): 225–36. http://dx.doi.org/10.1080/07408179608966269.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Irle, A. "Asymptotically optimal stopping rules in the presence of unknown parameters." Statistics & Probability Letters 30, no. 1 (September 1996): 9–16. http://dx.doi.org/10.1016/0167-7152(95)00195-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Martinsek, Adam T. "Comparison of some sequential procedures with related optimal stopping rules." Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete 70, no. 3 (1985): 411–16. http://dx.doi.org/10.1007/bf00534872.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Betrò, B., and F. Schoen. "Optimal and sub-optimal stopping rules for the Multistart algorithm in global optimization." Mathematical Programming 57, no. 1-3 (May 1992): 445–58. http://dx.doi.org/10.1007/bf01581094.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Bruss, F. Thomas, and Thomas S. Ferguson. "Multiple buying or selling with vector offers." Journal of Applied Probability 34, no. 4 (December 1997): 959–73. http://dx.doi.org/10.2307/3215010.

Full text

Abstract:

We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1, X2, · ··, be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, · ··, Nk, one for each component. The payoff is the sum over j of the jth component of minus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.

APA, Harvard, Vancouver, ISO, and other styles

30

Hill, Theodore P., and Arie Hordijk. "Selection of order of observation in optimal stopping problems." Journal of Applied Probability 22, no. 1 (March 1985): 177–84. http://dx.doi.org/10.2307/3213757.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

31

Hill, Theodore P., and Arie Hordijk. "Selection of order of observation in optimal stopping problems." Journal of Applied Probability 22, no. 01 (March 1985): 177–84. http://dx.doi.org/10.1017/s0021900200029107.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

32

Allaart, Pieter, and Michael Monticino. "Optimal Buy/Sell Rules for Correlated Random Walks." Journal of Applied Probability 45, no. 1 (March 2008): 33–44. http://dx.doi.org/10.1239/jap/1208358949.

Full text

Abstract:

Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.

APA, Harvard, Vancouver, ISO, and other styles

33

Allaart, Pieter, and Michael Monticino. "Optimal Buy/Sell Rules for Correlated Random Walks." Journal of Applied Probability 45, no. 01 (March 2008): 33–44. http://dx.doi.org/10.1017/s0021900200003934.

Full text

Abstract:

Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.

APA, Harvard, Vancouver, ISO, and other styles

34

Guo, X., and J. Liu. "Stopping at the maximum of geometric Brownian motion when signals are received." Journal of Applied Probability 42, no. 3 (September 2005): 826–38. http://dx.doi.org/10.1239/jap/1127322030.

Full text

Abstract:

Consider a geometric Brownian motion Xt(ω) with drift. Suppose that there is an independent source that sends signals at random times τ1 < τ2 < ⋯. Upon receiving each signal, a decision has to be made as to whether to stop or to continue. Stopping at time τ will bring a reward Sτ, where St = max(max0≤u≤tXu, s) for some constant s ≥ X0. The objective is to choose an optimal stopping time to maximize the discounted expected reward E[e−rτiSτi | X0 = x, S0 = s], where r is a discount factor. This problem can be viewed as a randomized version of the Bermudan look-back option pricing problem. In this paper, we derive explicit solutions to this optimal stopping problem, assuming that signal arrival is a Poisson process with parameter λ. Optimal stopping rules are differentiated by the frequency of the signal process. Specifically, there exists a threshold λ* such that if λ>λ*, the optimal stopping problem is solved via the standard formulation of a ‘free boundary’ problem and the optimal stopping time τ* is governed by a threshold a* such that τ* = inf{τn: Xτn≤a*Sτn}. If λ≤λ* then it is optimal to stop immediately a signal is received, i.e. at τ* = τ1. Mathematically, it is intriguing that a smooth fit is critical in the former case while irrelevant in the latter.

APA, Harvard, Vancouver, ISO, and other styles

35

Bather, J. A. "Search models." Journal of Applied Probability 29, no. 3 (September 1992): 605–15. http://dx.doi.org/10.2307/3214897.

Full text

Abstract:

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here we consider a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.

APA, Harvard, Vancouver, ISO, and other styles

36

Bather, J. A. "Search models." Journal of Applied Probability 29, no. 03 (September 1992): 605–15. http://dx.doi.org/10.1017/s0021900200043424.

Full text

Abstract:

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here we consider a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.

APA, Harvard, Vancouver, ISO, and other styles

37

Guo, X., and J. Liu. "Stopping at the maximum of geometric Brownian motion when signals are received." Journal of Applied Probability 42, no. 03 (September 2005): 826–38. http://dx.doi.org/10.1017/s0021900200000802.

Full text

Abstract:

Consider a geometric Brownian motion X t (ω) with drift. Suppose that there is an independent source that sends signals at random times τ 1 < τ 2 < ⋯. Upon receiving each signal, a decision has to be made as to whether to stop or to continue. Stopping at time τ will bring a reward S τ , where S t = max(max0≤u≤t X u , s) for some constant s ≥ X 0. The objective is to choose an optimal stopping time to maximize the discounted expected reward E[e−r τ i S τ i | X 0 = x, S 0 = s], where r is a discount factor. This problem can be viewed as a randomized version of the Bermudan look-back option pricing problem. In this paper, we derive explicit solutions to this optimal stopping problem, assuming that signal arrival is a Poisson process with parameter λ. Optimal stopping rules are differentiated by the frequency of the signal process. Specifically, there exists a threshold λ* such that if λ>λ*, the optimal stopping problem is solved via the standard formulation of a ‘free boundary’ problem and the optimal stopping time τ * is governed by a threshold a * such that τ * = inf{τ n : X τ n ≤a * S τ n }. If λ≤λ* then it is optimal to stop immediately a signal is received, i.e. at τ * = τ 1. Mathematically, it is intriguing that a smooth fit is critical in the former case while irrelevant in the latter.

APA, Harvard, Vancouver, ISO, and other styles

38

Ekström, Erik, and Ioannis Karatzas. "A sequential estimation problem with control and discretionary stopping." Probability, Uncertainty and Quantitative Risk 7, no. 3 (2022): 151. http://dx.doi.org/10.3934/puqr.2022011.

Full text

Abstract:

<p style='text-indent:20px;'>We show that “full-bang” control is optimal in a problem which combines features of (i) sequential least-squares <i>estimation</i> with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded <i>control</i> of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) “fast” discretionary <i>stopping</i>. We develop also the optimal filtering and stopping rules in this context.</p>

APA, Harvard, Vancouver, ISO, and other styles

39

Yeh, Tzu-Sheng. "APPROXIMATION TO OPTIMAL STOPPING RULES FOR WEIBULL RANDOM VARIABLES WITH UNKNOWN SCALE PARAMETER." Taiwanese Journal of Mathematics 9, no. 4 (December 2005): 721–32. http://dx.doi.org/10.11650/twjm/1500407892.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Siegrist, Kyle. "Estimation and optimal stopping in a debugging model with masking." Journal of Applied Probability 22, no. 2 (June 1985): 336–45. http://dx.doi.org/10.2307/3213777.

Full text

Abstract:

A system has an irremovable failure source and a number of removable flaws. The system undergoes a sequence of trials designed to detect and remove the flaws. On each trial, the irremovable failure source may cause failure which in turn may block the detection of any flaws. If not, then each flaw in the system, independently, is detected on that trial with a certain probability and each detected flaw, independently, is removed from the system with a certain probability before the next trial. Distributions of the outcomes of the trials are obtained. Point estimates of the parameters, based on accumulated trial data, are given. Assuming that certain costs are associated with trials, optimal stopping rules and a cost-benefit analysis are given.

APA, Harvard, Vancouver, ISO, and other styles

41

Siegrist, Kyle. "Estimation and optimal stopping in a debugging model with masking." Journal of Applied Probability 22, no. 02 (June 1985): 336–45. http://dx.doi.org/10.1017/s0021900200037803.

Full text

Abstract:

A system has an irremovable failure source and a number of removable flaws. The system undergoes a sequence of trials designed to detect and remove the flaws. On each trial, the irremovable failure source may cause failure which in turn may block the detection of any flaws. If not, then each flaw in the system, independently, is detected on that trial with a certain probability and each detected flaw, independently, is removed from the system with a certain probability before the next trial. Distributions of the outcomes of the trials are obtained. Point estimates of the parameters, based on accumulated trial data, are given. Assuming that certain costs are associated with trials, optimal stopping rules and a cost-benefit analysis are given.

APA, Harvard, Vancouver, ISO, and other styles

42

Bruss, F. Thomas, and Thomas S. Ferguson. "Multiple buying or selling with vector offers." Journal of Applied Probability 34, no. 04 (December 1997): 959–73. http://dx.doi.org/10.1017/s0021900200101652.

Full text

Abstract:

We consider a generalization of the house-selling problem to sellingkhouses. Let the offers,X1,X2, · ··,be independent, identically distributedk-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneouslykstopping rules,N1, · ··,Nk,one for each component. The payoff is the sum overjof thejth component ofminus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.

APA, Harvard, Vancouver, ISO, and other styles

43

Allaart, Pieter C. "Optimal Stopping Rules for American and Russian Options in a Correlated Random Walk Model." Stochastic Models 26, no. 4 (November 5, 2010): 594–616. http://dx.doi.org/10.1080/15326349.2010.519667.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Plato, R., and U. Hämarik. "On pseudo—optimal parameter choices and stopping rules for regularization methods in banach spaces∗." Numerical Functional Analysis and Optimization 17, no. 1-2 (January 1996): 181–95. http://dx.doi.org/10.1080/01630569608816690.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Assaf, David, and Ester Samuel-Cahn. "Optimal cooperative stopping rules for maximization of the product of the expected stopped values." Statistics & Probability Letters 38, no. 1 (May 1998): 89–99. http://dx.doi.org/10.1016/s0167-7152(97)00158-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Yeh, Tzu-Sheng, and Shen-Ming Lee. "APPROXIMATION TO OPTIMAL STOPPING RULES FOR GUMBEL RANDOM VARIABLES WITH UNKNOWN LOCATION AND SCALE PARAMETERS." Taiwanese Journal of Mathematics 10, no. 4 (June 2006): 1047–67. http://dx.doi.org/10.11650/twjm/1500403892.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Chen, Juei-Chao, and Shen-Ming Lee. "APPROXIMATION TO OPTIMAL STOPPING RULES FOR GAMMA RANDOM VARIABLES WITH UNKNOWN LOCATION AND SCALE PARAMETERS." Communications in Statistics - Theory and Methods 30, no. 4 (March 31, 2001): 775–84. http://dx.doi.org/10.1081/sta-100002151.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Moatti, M., S. Zohar, W. F. Rosenberger, and S. Chevret. "A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes." Methods of Information in Medicine 55, no. 01 (2016): 4–13. http://dx.doi.org/10.3414/me14-01-0132.

Full text

Abstract:

SummaryBackground: Response-adaptive randomisation designs have been proposed to im -prove the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosen -berger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. Objectives: The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the esti -mated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by re -designing a clinical trial on multiple myeloma. Methods: To handle continuous monitoring of data, we propose a Bayesian response-adap -tive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simu lationstudy to assess and compare the perform -ance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive – either frequentist or fully Bayesian – designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior dis -tribution of the log hazard ratio were com -puted. The method is then illus trated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. Results: As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mix -ture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Conclusions: Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

APA, Harvard, Vancouver, ISO, and other styles

49

Tamaki, Mitsushi. "Urn sampling distributions giving alternate correspondences between two optimal stopping problems." Advances in Applied Probability 48, no. 3 (September 2016): 726–43. http://dx.doi.org/10.1017/apr.2016.25.

Full text

Abstract:

Abstract The best-choice problem and the duration problem, known as versions of the secretary problem, are concerned with choosing an object from those that appear sequentially. Let (B,p) denote the best-choice problem and (D,p) the duration problem when the total number N of objects is a bounded random variable with prior p=(p1, p2,...,pn) for a known upper bound n. Gnedin (2005) discovered the correspondence relation between these two quite different optimal stopping problems. That is, for any given prior p, there exists another prior q such that (D,p) is equivalent to (B,q). In this paper, motivated by his discovery, we attempt to find the alternate correspondence {p(m),m≥0}, i.e. an infinite sequence of priors such that (D,p(m-1)) is equivalent to (B,p(m)) for all m≥1, starting with p(0)=(0,...,0,1). To be more precise, the duration problem is distinguished into (D1,p) or (D2,p), referred to as model 1 or model 2, depending on whether the planning horizon is N or n. The aforementioned problem is model 1. For model 2 as well, we can find the similar alternate correspondence {p[m],m≥ 0}. We treat both the no-information model and the full-information model and examine the limiting behaviors of their optimal rules and optimal values related to the alternate correspondences as n→∞. A generalization of the no-information model is given. It is worth mentioning that the alternate correspondences for model 1 and model 2 are respectively related to the urn sampling models without replacement and with replacement.

APA, Harvard, Vancouver, ISO, and other styles

50

Samuels, Stephen M. "Why do these quite different best-choice problems have the same solutions?" Advances in Applied Probability 36, no. 2 (June 2004): 398–416. http://dx.doi.org/10.1239/aap/1086957578.

Full text

Abstract:

The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of n i.i.d. standard uniform random variables. Porosiński, in 1987, replaced a fixed n by a random N, uniform on {1,2,…,n} and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosiński compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosiński-Petruccelli stopping rule, and the full-information ‘duration of holding the best’ problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosiński problem in disguise.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!