A general method for finding the optimal threshold in discrete time

Christensen, Sören; Irle, Albrecht

doi:10.1080/17442508.2018.1541991

Cited by 8 publications

(6 citation statements)

References 36 publications

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“…Villeneuve () gives sufficient conditions to have threshold optimal strategies, and Arkin () gives necessary and sufficient conditions for Itô diffusions with C 2 payoffs functions to have one‐sided solutions, whereas Arkin and Slastnikov () and Crocce and Mordecki () give also necessary and sufficient conditions in different and more general diffusion frameworks. For more general Markov processes, Christensen and Irle (), Christensen, Salminen, and Ta (), and Mordecki and Salminen () propose verification results for one‐sided solutions, but also for problems where the optimal stopping time is of the form

τ^{*} = inf false{t \geq 0 0pt: X (t) \notin (x_{*}, x^{*}) false} .

…”

Section: Introductionmentioning

confidence: 99%

Optimal stopping of Brownian motion with broken drift

Mordecki¹,

Salminen

2019

High Frequency

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We solve an optimal stopping problem where the underlying diffusion is Brownian motion on boldR with a positive piecewise constant drift changing at zero. It is assumed that the drift μ1 on the negative side is smaller than the drift μ2 on the positive side. The main observation is that if μ2−μ1>1/2, then there exist values of the discounting parameter for which it is not optimal to stop in the vicinity of zero where the drift changes. However, when the discounting gets larger, the stopping region becomes connected and contains zero. This is in contrast with results concerning optimal stopping of skew Brownian motion where the skew point is for all values of the discounting parameter in the continuation region in case the skew parameter is bigger than 1/2. In all cases, a practical implementation of these optimal stopping strategies, based on hitting times of boundaries of continuation regions, would require access to the highest‐possible frequency data which is consistent with the continuous‐time modeling framework.

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τ^{*} = inf false{t \geq 0 0pt: X (t) \notin (x_{*}, x^{*}) false} .

…”

Section: Introductionmentioning

confidence: 99%

Optimal stopping of Brownian motion with broken drift

Mordecki¹,

Salminen

2019

High Frequency

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“…After the present paper had been submitted, a referee brought to our attention the article by Christensen and Irle [5]. (Note that both [5] and the original version [14] of the present paper were posted on arxiv in October 2017.) The authors proposed a general method for finding the optimal threshold for discrete-time optimal stopping problems with general underlying Markov processes {X n } n≥0 .…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

One-sided solutions for optimal stopping problems with logconcave reward functions

Lin

Yao

2019

Adv. Appl. Probab.

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In the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including (and K > 0) under general random walks in discrete time and Lévy processes in continuous time (subject to mild integrability conditions). All of such reward functions are continuous, increasing and logconcave while the corresponding optimal stopping times are of threshold type (i.e. the solutions are one-sided). In this paper, we show that all optimal stopping problems with increasing, logconcave and right-continuous reward functions admit one-sided solutions for general random walks and Lévy processes. We also investigate in detail the principle of smooth fit for Lévy processes when the reward function is increasing and logconcave.

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“…Each regression model comprised of a threshold model, u = g(a j ),u j with u denoting the thresholds, and g(a j ) a linear function with parameters a j . Following the nature of the questions, a symmetric structure was specified for the threshold parameters so that only two parameters (a j ) had to be estimated, the central threshold, and a spacing between the response levels we determined (Christensen and Irle 2019); and a group effect with the coefficient of b 1 representing the difference of group 2 (without facilitated dialogue) relative to group 1 (with facilitated dialogue). This group difference thus represents an estimation of the influence of characteristics that are different in the two groups on the two questions we investigate.…”

Section: Pre and Post Demo Surveysmentioning

confidence: 99%

Power to the facilitated agricultural dialogue: an analysis of on-farm demonstrations as transformative learning spaces

Cooreman¹,

Debruyne²,

Vandenabeele

et al. 2021

The Journal of Agricultural Education and Extension

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Purpose: It remains a critical question how to support farmers to develop towards more sustainable practices. Earlier experiences reveal that on-farm demonstrations (OFDs) can be part of the answer. Therefore, we investigate OFDs as potential transformative learning spaces. Methodology: We apply a mixed methods approach, using an observation tool, participant surveys and telephone interviews. We compare 15 different OFDs, divided into two groups: OFDs with and without facilitated dialogue. We investigated differences based on core inducing processes of transformative learning: disorienting dilemma and (self-)reflection. Additionally we investigated the adoption decision making process half a year after the OFD took place. Findings: Participants in facilitated dialogue OFDs agreed significantly more on experiencing surprise, an indication of disorienting dilemma, and on having reflected and learned. Most mentioned adoption barriers are a lack of relevance for the specific situation and a need for more information. Most mentioned suggestions indicate a request for more real life application. Practical implications: This research indicates that OFDs with facilitated dialogue can trigger more cognitive conflict and reflection processes of attendees, and thus support learning processes on (more) sustainable agricultural practices, as opposed to OFDs without deliberate dialogue facilitation. Theoretical implications: Our study demonstrates that transformative learning theory can inform research on agricultural learning spaces, such as OFDs, on effective triggers to support learning and competencies towards more sustainable agriculture. Originality: Based on rich empirical quantitative and qualitative data we reveal that facilitated dialogue enhances learning during OFDs, but this does not seem to be a common practice.

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A general method for finding the optimal threshold in discrete time

Cited by 8 publications

References 36 publications

Optimal stopping of Brownian motion with broken drift

Optimal stopping of Brownian motion with broken drift

One-sided solutions for optimal stopping problems with logconcave reward functions

Power to the facilitated agricultural dialogue: an analysis of on-farm demonstrations as transformative learning spaces

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