We investigate branching processes in varying environment, for which $overline{f}_n to 1$ and $sum_{n=1}^infty (1-overline{f}_n)_+ = infty$ , $sum_{n=1}^infty (overline{f}_n - 1)_+ < infty$ , where $overline{f}_n$ stands for the offspring mean in generation n. Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on nonextinction, and adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting (2020).
我们研究了变化环境中的分支过程，对于这种过程，$overline{f}_n to 1$，$sum_{n=1}^infty (1-overline{f}_n)_+ = infty$，$sum_{n=1}^infty (overline{f}_n - 1)_+ < infty$，其中$overline{f}_n$代表第 n 代的后代平均值。由于亚临界状态占主导地位，这种过程几乎肯定会消亡，因此，为了得到一个非微观极限，我们考虑了两种情况：以不消亡为条件，以及增加移民。在这两种情况下，我们都证明了该过程在分布上无需归一化即可收敛到非退化的复合泊松极限规律。证明依赖于 Kersting（2020 年）提出的形状函数技术。
{"title":"Branching processes in nearly degenerate varying environment","authors":"Péter Kevei, Kata Kubatovics","doi":"10.1017/jpr.2024.15","DOIUrl":"https://doi.org/10.1017/jpr.2024.15","url":null,"abstract":"We investigate branching processes in varying environment, for which <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline1.png\"/> <jats:tex-math> $overline{f}_n to 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline2.png\"/> <jats:tex-math> $sum_{n=1}^infty (1-overline{f}_n)_+ = infty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline3.png\"/> <jats:tex-math> $sum_{n=1}^infty (overline{f}_n - 1)_+ < infty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline4.png\"/> <jats:tex-math> $overline{f}_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> stands for the offspring mean in generation <jats:italic>n</jats:italic>. Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on nonextinction, and adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting (2020).","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"JPR volume 61 issue 2 Cover and Front matter","authors":"","doi":"10.1017/jpr.2024.4","DOIUrl":"https://doi.org/10.1017/jpr.2024.4","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141016397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"JPR volume 61 issue 2 Cover and Back matter","authors":"","doi":"10.1017/jpr.2024.5","DOIUrl":"https://doi.org/10.1017/jpr.2024.5","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141017515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qu, Dassios, and Zhao (2021) suggested an exact simulation method for tempered stable Ornstein–Uhlenbeck processes, but their algorithms contain some errors. This short note aims to correct their algorithms and conduct some numerical experiments.
{"title":"A remark on exact simulation of tempered stable Ornstein–Uhlenbeck processes","authors":"Takuji Arai, Yuto Imai","doi":"10.1017/jpr.2024.17","DOIUrl":"https://doi.org/10.1017/jpr.2024.17","url":null,"abstract":"Qu, Dassios, and Zhao (2021) suggested an exact simulation method for tempered stable Ornstein–Uhlenbeck processes, but their algorithms contain some errors. This short note aims to correct their algorithms and conduct some numerical experiments.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Eaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible, which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton’s Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean.
{"title":"Recurrence and transience of a Markov chain on + and evaluation of prior distributions for a Poisson mean","authors":"J. Hobert, K. Khare","doi":"10.1017/jpr.2024.13","DOIUrl":"https://doi.org/10.1017/jpr.2024.13","url":null,"abstract":"\u0000 Eaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible, which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton’s Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140658130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We explore the limiting spectral distribution of large-dimensional random permutation matrices, assuming the underlying population distribution possesses a general dependence structure. Let $textbf X = (textbf x_1,ldots,textbf x_n)$ $in mathbb{C} ^{m times n}$ be an $m times n$ data matrix after self-normalization (n samples and m features), where $textbf x_j = (x_{1j}^{*},ldots, x_{mj}^{*} )^{*}$ . Specifically, we generate a permutation matrix $textbf X_pi$ by permuting the entries of $textbf x_j$ $(j=1,ldots,n)$ and demonstrate that the empirical spectral distribution of $textbf {B}_n = ({m}/{n})textbf{U} _{n} textbf{X} _pi textbf{X} _pi^{*} textbf{U} _{n}^{*}$ weakly converges to the generalized Marčenko–Pastur distribution with probability 1, where $textbf{U} _n$
我们探讨了大维随机置换矩阵的极限谱分布，假设底层种群分布具有一般的依赖结构。让 $textbf X = (textbf x_1,ldots,textbf x_n)$$in mathbb{C} 是一个 $m times n} 的数据矩阵。^{m times n}$ 是自归一化（n 个样本和 m 个特征）后的 $m times n$ 数据矩阵，其中 $textbf x_j = (x_{1j}^{*},ldots, x_{mj}^{*} )^{*}$。具体来说，我们通过对 $textbf x_j$ (j=1,ldots,n)$ 的条目进行置换，生成一个置换矩阵 $textbf X_pi$，并证明了 $textbf {B}_n = ({m}/{n})textbf{U} 的经验谱分布。_{n}textbf{X} _pi textbf{X} _pi^{*}textbf{U} _{n} textbf{X} _pi^{*}_{n}^{*}$ 弱收敛于概率为 1 的广义马尔琴科-帕斯图分布，其中 $textbf{U} _n$ 是$textbf{U}的序列。_n$ 是一个 $p times m$ 非随机复矩阵序列。我们需要的条件是 $p/n to c >0$ 和 $m/n to gamma > 0$ 。
{"title":"The limiting spectral distribution of large random permutation matrices","authors":"Jianghao Li, Huanchao Zhou, Zhidong Bai, Jiang Hu","doi":"10.1017/jpr.2024.8","DOIUrl":"https://doi.org/10.1017/jpr.2024.8","url":null,"abstract":"We explore the limiting spectral distribution of large-dimensional random permutation matrices, assuming the underlying population distribution possesses a general dependence structure. Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline1.png\" /> <jats:tex-math> $textbf X = (textbf x_1,ldots,textbf x_n)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline2.png\" /> <jats:tex-math> $in mathbb{C} ^{m times n}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be an <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline3.png\" /> <jats:tex-math> $m times n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> data matrix after self-normalization (<jats:italic>n</jats:italic> samples and <jats:italic>m</jats:italic> features), where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline4.png\" /> <jats:tex-math> $textbf x_j = (x_{1j}^{*},ldots, x_{mj}^{*} )^{*}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Specifically, we generate a permutation matrix <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline5.png\" /> <jats:tex-math> $textbf X_pi$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> by permuting the entries of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline6.png\" /> <jats:tex-math> $textbf x_j$ </jats:tex-math> </jats:alternatives> </jats:inline-formula><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline7.png\" /> <jats:tex-math> $(j=1,ldots,n)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and demonstrate that the empirical spectral distribution of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline8.png\" /> <jats:tex-math> $textbf {B}_n = ({m}/{n})textbf{U} _{n} textbf{X} _pi textbf{X} _pi^{*} textbf{U} _{n}^{*}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> weakly converges to the generalized Marčenko–Pastur distribution with probability 1, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000081_inline9.png\" /> <jats:tex-math> $textbf{U} _n$","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aizelle Abelgas, Bryan Carrillo, John Palacios, David Weisbart, Adam M. Yassine
A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand–Diguet–Puiseux theorem establishes between Gaussian curvature and both circumference and area deficits.
{"title":"Buffon’s problem determines Gaussian curvature in three geometries","authors":"Aizelle Abelgas, Bryan Carrillo, John Palacios, David Weisbart, Adam M. Yassine","doi":"10.1017/jpr.2023.114","DOIUrl":"https://doi.org/10.1017/jpr.2023.114","url":null,"abstract":"A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand–Diguet–Puiseux theorem establishes between Gaussian curvature and both circumference and area deficits.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $mathcal{C}$ denote the family of all coherent distributions on the unit square $[0,1]^2$ , i.e. all those probability measures $mu$ for which there exists a random vector $(X,Y)sim mu$ , a pair $(mathcal{G},mathcal{H})$ of $sigma$ -fields, and an event E such that $X=mathbb{P}(Emidmathcal{G})$ , $Y=mathbb{P}(Emidmathcal{H})$ almost surely. We examine the set $mathrm{ext}(mathcal{C})$ of extreme points of $mathcal{C}$ and provide its general characterisation. Moreover, we establish sever
{"title":"Coherent distributions on the square–extreme points and asymptotics","authors":"Stanisław Cichomski, Adam Osękowski","doi":"10.1017/jpr.2024.1","DOIUrl":"https://doi.org/10.1017/jpr.2024.1","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline1.png\" /> <jats:tex-math> $mathcal{C}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> denote the family of all coherent distributions on the unit square <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline2.png\" /> <jats:tex-math> $[0,1]^2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, i.e. all those probability measures <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline3.png\" /> <jats:tex-math> $mu$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for which there exists a random vector <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline4.png\" /> <jats:tex-math> $(X,Y)sim mu$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, a pair <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline5.png\" /> <jats:tex-math> $(mathcal{G},mathcal{H})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline6.png\" /> <jats:tex-math> $sigma$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-fields, and an event <jats:italic>E</jats:italic> such that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline7.png\" /> <jats:tex-math> $X=mathbb{P}(Emidmathcal{G})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline8.png\" /> <jats:tex-math> $Y=mathbb{P}(Emidmathcal{H})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> almost surely. We examine the set <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline9.png\" /> <jats:tex-math> $mathrm{ext}(mathcal{C})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of extreme points of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000019_inline10.png\" /> <jats:tex-math> $mathcal{C}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and provide its general characterisation. Moreover, we establish sever","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ze-An Ng, You-Beng Koh, Tee-How Loo, Hailiang Yang
We consider the super-replication problem for a class of exotic options known as life-contingent options within the framework of the Black–Scholes market model. The option is allowed to be exercised if the death of the option holder occurs before the expiry date, otherwise there is a compensation payoff at the expiry date. We show that there exists a minimal super-replication portfolio and determine the associated initial investment. We then give a characterisation of when replication of the option is possible. Finally, we give an example of an explicit super-replicating hedge for a simple life-contingent option.
{"title":"Super-replication of life-contingent options under the Black–Scholes framework","authors":"Ze-An Ng, You-Beng Koh, Tee-How Loo, Hailiang Yang","doi":"10.1017/jpr.2024.10","DOIUrl":"https://doi.org/10.1017/jpr.2024.10","url":null,"abstract":"We consider the super-replication problem for a class of exotic options known as life-contingent options within the framework of the Black–Scholes market model. The option is allowed to be exercised if the death of the option holder occurs before the expiry date, otherwise there is a compensation payoff at the expiry date. We show that there exists a minimal super-replication portfolio and determine the associated initial investment. We then give a characterisation of when replication of the option is possible. Finally, we give an example of an explicit super-replicating hedge for a simple life-contingent option.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times, and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions for the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.
{"title":"Constrained optimal stopping under a regime-switching model","authors":"Takuji Arai, Masahiko Takenaka","doi":"10.1017/jpr.2023.122","DOIUrl":"https://doi.org/10.1017/jpr.2023.122","url":null,"abstract":"<p>We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times, and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions for the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：