Optimal variance stopping with linear diffusions

Department of Mathematical Sciences

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Optimal variance stopping with linear diffusions. / Gad, Kamille Sofie Tågholt; Matomäki, Pekka.

In: Stochastic Processes and Their Applications, Vol. 130, No. 4, 2020, p. 2349-2383.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Gad, KST & Matomäki, P 2020, 'Optimal variance stopping with linear diffusions', Stochastic Processes and Their Applications, vol. 130, no. 4, pp. 2349-2383. https://doi.org/10.1016/j.spa.2019.07.001

APA

Gad, K. S. T., & Matomäki, P. (2020). Optimal variance stopping with linear diffusions. Stochastic Processes and Their Applications, 130(4), 2349-2383. https://doi.org/10.1016/j.spa.2019.07.001

Vancouver

Gad KST, Matomäki P. Optimal variance stopping with linear diffusions. Stochastic Processes and Their Applications. 2020;130(4):2349-2383. https://doi.org/10.1016/j.spa.2019.07.001

Author

Gad, Kamille Sofie Tågholt ; Matomäki, Pekka. / Optimal variance stopping with linear diffusions. In: Stochastic Processes and Their Applications. 2020 ; Vol. 130, No. 4. pp. 2349-2383.

Bibtex

@article{7002221919c9465bb3002129b4aff77f,

title = "Optimal variance stopping with linear diffusions",

abstract = "We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.",

keywords = "Infinite zero-sum game, Linear diffusion, Non-linear optimal stopping, Optimal stopping, Variance",

author = "Gad, {Kamille Sofie T{\aa}gholt} and Pekka Matom{\"a}ki",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2020",

doi = "10.1016/j.spa.2019.07.001",

language = "English",

volume = "130",

pages = "2349--2383",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier BV * North-Holland",

number = "4",

}

RIS

TY - JOUR

T1 - Optimal variance stopping with linear diffusions

AU - Gad, Kamille Sofie Tågholt

AU - Matomäki, Pekka

PY - 2020

Y1 - 2020

N2 - We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.

AB - We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.

KW - Infinite zero-sum game

KW - Linear diffusion

KW - Non-linear optimal stopping

KW - Optimal stopping

KW - Variance

UR - http://www.scopus.com/inward/record.url?scp=85069709896&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2019.07.001

DO - 10.1016/j.spa.2019.07.001

M3 - Journal article

AN - SCOPUS:85069709896

VL - 130

SP - 2349

EP - 2383

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 4

ER -

ID: 269517534