Pub Date : 2024-10-17DOI: 10.1016/j.spl.2024.110283
Paek Il-Kwang , Kang Chol-Su , Kim Kyong-Hui
This paper deals with new explicit pricing formulae for Lookback option when underlying asset price processes are represented by stochastic delay differential equation (hereafter “SDDE”). We derive a lemma on the joint distribution of the minimum and itself of a Wiener process in the SDDE model. Using this lemma, we obtain the explicit pricing formulae for the Lookback option. Through some numerical comparison experiment, we assure the correctness of the obtained pricing formula.
{"title":"Pricing formula of Lookback option in stochastic delay differential equation model","authors":"Paek Il-Kwang , Kang Chol-Su , Kim Kyong-Hui","doi":"10.1016/j.spl.2024.110283","DOIUrl":"10.1016/j.spl.2024.110283","url":null,"abstract":"<div><div>This paper deals with new explicit pricing formulae for Lookback option when underlying asset price processes are represented by stochastic delay differential equation (hereafter “SDDE”). We derive a lemma on the joint distribution of the minimum and itself of a Wiener process in the SDDE model. Using this lemma, we obtain the explicit pricing formulae for the Lookback option. Through some numerical comparison experiment, we assure the correctness of the obtained pricing formula.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110283"},"PeriodicalIF":0.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527950","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}
Pub Date : 2024-10-15DOI: 10.1016/j.spl.2024.110285
Soham Gokhale
We consider the stochastic Landau–Lifshitz–Gilbert equation driven by pure jump noise. We assume non-zero contribution from the helicity term to the total energy. Using finite dimensional approximation followed by a generalization of the Jakubowski’s version of the Skorohod Theorem for non-metric spaces, we show that the considered problem admits a weak martingale solution. Restricting the problem to dimension 1, we show that the obtained solution is pathwise unique, thereby concluding the existence of a strong solution.
{"title":"Well-posedness for the stochastic Landau–Lifshitz–Gilbert equation with helicity driven by jump noise","authors":"Soham Gokhale","doi":"10.1016/j.spl.2024.110285","DOIUrl":"10.1016/j.spl.2024.110285","url":null,"abstract":"<div><div>We consider the stochastic Landau–Lifshitz–Gilbert equation driven by pure jump noise. We assume non-zero contribution from the helicity term to the total energy. Using finite dimensional approximation followed by a generalization of the Jakubowski’s version of the Skorohod Theorem for non-metric spaces, we show that the considered problem admits a weak martingale solution. Restricting the problem to dimension 1, we show that the obtained solution is pathwise unique, thereby concluding the existence of a strong solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110285"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527949","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}
Pub Date : 2024-10-15DOI: 10.1016/j.spl.2024.110284
Ryan McFadden, Fraser Daly, Seva Shneer
We consider a susceptible-infected-susceptible (SIS) epidemic model on an undirected graph, with a homogeneous infection rate and heterogeneous curing rates. We set an overall network curing rate, , and study optimal allocation of curing rates to nodes, in terms of the expected time to the extinction of the epidemic. As other parameters are fixed, we study these allocations as the infection rate tends to 0 and in both regular and non-regular graphs. We further illustrate this optimisation with some numerical examples. Our findings demonstrate that, while the uniform split of is optimal in some situations, it is typically not optimal, even for regular graphs.
{"title":"Optimal curing rate allocation in the SIS epidemic model","authors":"Ryan McFadden, Fraser Daly, Seva Shneer","doi":"10.1016/j.spl.2024.110284","DOIUrl":"10.1016/j.spl.2024.110284","url":null,"abstract":"<div><div>We consider a susceptible-infected-susceptible (SIS) epidemic model on an undirected graph, with a homogeneous infection rate and heterogeneous curing rates. We set an overall network curing rate, <span><math><mi>Δ</mi></math></span>, and study optimal allocation of curing rates to nodes, in terms of the expected time to the extinction of the epidemic. As other parameters are fixed, we study these allocations as the infection rate tends to 0 and <span><math><mi>∞</mi></math></span> in both regular and non-regular graphs. We further illustrate this optimisation with some numerical examples. Our findings demonstrate that, while the uniform split of <span><math><mi>Δ</mi></math></span> is optimal in some situations, it is typically not optimal, even for regular graphs.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110284"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.spl.2024.110286
Dingwen Zhang
Low-frequency observations are a common occurrence in real-world applications, making statistical inference for stochastic processes driven by stochastic differential equations (SDEs) based on such observations an important issue. In this paper, we investigate the statistical inference for the Ornstein–Uhlenbeck (OU) process using low-frequency observations. We propose modified least squares estimators (MLSEs) for the drift parameters and a modified quadratic variation estimator for the diffusion parameter based on the solution of the OU process. The MLSEs are derived heuristically using the nonlinear least squares method, despite the OU process satisfying a linear SDE. Unlike previous approaches, these modified estimators are asymptotically unbiased. Leveraging the ergodic properties of the OU process, we also propose ergodic estimators for the three parameters. The asymptotic behavior of these estimators is established using the ergodic properties and central limit theorem for the OU process, achieved through linear model techniques and multivariate Markov chain central limit theorem. Monte Carlo simulation results are presented to illustrate and support our theoretical findings.
低频观测是现实世界应用中的常见现象，因此基于低频观测对由随机微分方程（SDE）驱动的随机过程进行统计推断是一个重要问题。本文研究了利用低频观测数据对奥恩斯坦-乌伦贝克（OU）过程进行统计推断的问题。我们根据 OU 过程的解，提出了漂移参数的修正最小二乘估计器（MLSE）和扩散参数的修正二次变化估计器。尽管 OU 过程满足线性 SDE，但 MLSE 是通过非线性最小二乘法启发式得出的。与以前的方法不同，这些修正估计器在渐近上是无偏的。利用 OU 过程的遍历特性，我们还提出了三个参数的遍历估计值。通过线性模型技术和多变量马尔可夫链中心极限定理，我们利用 OU 过程的遍历特性和中心极限定理确定了这些估计器的渐近行为。蒙特卡罗模拟结果用于说明和支持我们的理论发现。
{"title":"Statistical inference for Ornstein–Uhlenbeck processes based on low-frequency observations","authors":"Dingwen Zhang","doi":"10.1016/j.spl.2024.110286","DOIUrl":"10.1016/j.spl.2024.110286","url":null,"abstract":"<div><div>Low-frequency observations are a common occurrence in real-world applications, making statistical inference for stochastic processes driven by stochastic differential equations (SDEs) based on such observations an important issue. In this paper, we investigate the statistical inference for the Ornstein–Uhlenbeck (OU) process using low-frequency observations. We propose modified least squares estimators (MLSEs) for the drift parameters and a modified quadratic variation estimator for the diffusion parameter based on the solution of the OU process. The MLSEs are derived heuristically using the nonlinear least squares method, despite the OU process satisfying a linear SDE. Unlike previous approaches, these modified estimators are asymptotically unbiased. Leveraging the ergodic properties of the OU process, we also propose ergodic estimators for the three parameters. The asymptotic behavior of these estimators is established using the ergodic properties and central limit theorem for the OU process, achieved through linear model techniques and multivariate Markov chain central limit theorem. Monte Carlo simulation results are presented to illustrate and support our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110286"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527948","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}
Pub Date : 2024-10-11DOI: 10.1016/j.spl.2024.110282
Rajeev Bhaskaran, Stefan Tappe
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a connection to SPDEs in continuously embedded spaces.
{"title":"A note on invariant manifolds for stochastic partial differential equations in the framework of the variational approach","authors":"Rajeev Bhaskaran, Stefan Tappe","doi":"10.1016/j.spl.2024.110282","DOIUrl":"10.1016/j.spl.2024.110282","url":null,"abstract":"<div><div>In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a connection to SPDEs in continuously embedded spaces.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110282"},"PeriodicalIF":0.9,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.spl.2024.110281
Kang Wang , Na Zou , Hong Qin
In this paper, we extend the study of wordlength enumerator to asymmetrical designs, and unify the generalized - and -wordlength pattern with generalized wordlength enumerator. The generalized wordlength enumerator is easy and fast to compute, and can effectively compare and rank symmetrical and asymmetrical designs. A lower bound of generalized wordlength enumerator is provided, and can be used as a benchmark for searching and constructing optimal designs. Numerical results are also provided, which lend further support to our theoretical findings.
{"title":"Generalized wordlength enumerator for asymmetrical designs","authors":"Kang Wang , Na Zou , Hong Qin","doi":"10.1016/j.spl.2024.110281","DOIUrl":"10.1016/j.spl.2024.110281","url":null,"abstract":"<div><div>In this paper, we extend the study of wordlength enumerator to asymmetrical designs, and unify the generalized <span><math><mi>α</mi></math></span>- and <span><math><mi>β</mi></math></span>-wordlength pattern with generalized wordlength enumerator. The generalized wordlength enumerator is easy and fast to compute, and can effectively compare and rank symmetrical and asymmetrical designs. A lower bound of generalized wordlength enumerator is provided, and can be used as a benchmark for searching and constructing optimal designs. Numerical results are also provided, which lend further support to our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110281"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593992","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}
Pub Date : 2024-10-01DOI: 10.1016/j.spl.2024.110280
Jiang Cheng , Chao Deng , Shuyan Liu , Xudong Zeng
Reinsurance is the insurance of insurance companies. We develop a dynamic equilibrium model for reinsurance pricing based on the supply and demand of reinsurance. In the model, an insurance company and a reinsurance company make decisions on the optimal reinsurance policy as a demander and a supplier of reinsurance, respectively. The reinsurance price is determined when the demand matches the supply. We incorporate the proportional reinsurance policy as well as investment opportunities into the framework. The high flexibility of this equilibrium pricing model paves a new way for studies of optimal reinsurance and reinsurance pricing.
{"title":"An equilibrium model of reinsurance pricing","authors":"Jiang Cheng , Chao Deng , Shuyan Liu , Xudong Zeng","doi":"10.1016/j.spl.2024.110280","DOIUrl":"10.1016/j.spl.2024.110280","url":null,"abstract":"<div><div>Reinsurance is the insurance of insurance companies. We develop a dynamic equilibrium model for reinsurance pricing based on the supply and demand of reinsurance. In the model, an insurance company and a reinsurance company make decisions on the optimal reinsurance policy as a demander and a supplier of reinsurance, respectively. The reinsurance price is determined when the demand matches the supply. We incorporate the proportional reinsurance policy as well as investment opportunities into the framework. The high flexibility of this equilibrium pricing model paves a new way for studies of optimal reinsurance and reinsurance pricing.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110280"},"PeriodicalIF":0.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417135","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}
Pub Date : 2024-09-27DOI: 10.1016/j.spl.2024.110279
Kai Wang , Hongjie Fan , Yanling Zhu
In this paper, we propose and investigate the stochastic SIRI epidemic model with two generalized incidence rate functions. We firstly study the existence and uniqueness of the globally positive solution to the stochastic SIRI model with positive initial value. Then we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Meanwhile, we obtain that the solution to the stochastic model has a unique stationary distribution when is greater than one. Our results show that the intensity of white noise can affect the dynamical behaviors of the model. Finally, we use numerical simulation to illustrate theoretical results, and apply both the stochastic and deterministic models to analyze the outbreak of COVID-19 epidemic in Serbia.
本文提出并研究了具有两个广义发病率函数的随机 SIRI 流行模型。我们首先研究了具有正初始值的随机 SIRI 模型全局正解的存在性和唯一性。然后，我们得到了随机流行模型中疾病消亡的充分条件，并发现大噪声会使疾病以指数形式消亡。同时，我们得到当 R0s˜ 大于 1 时，随机模型的解具有唯一的静态分布。我们的结果表明，白噪声的强度会影响模型的动力学行为。最后，我们用数值模拟来说明理论结果，并应用随机模型和确定性模型来分析塞尔维亚 COVID-19 疫情的爆发。
{"title":"Stationary distribution of a stochastic generalized SIRI epidemic model with reinfection and relapse","authors":"Kai Wang , Hongjie Fan , Yanling Zhu","doi":"10.1016/j.spl.2024.110279","DOIUrl":"10.1016/j.spl.2024.110279","url":null,"abstract":"<div><div>In this paper, we propose and investigate the stochastic SIRI epidemic model with two generalized incidence rate functions. We firstly study the existence and uniqueness of the globally positive solution to the stochastic SIRI model with positive initial value. Then we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Meanwhile, we obtain that the solution to the stochastic model has a unique stationary distribution when <span><math><mover><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup></mrow><mrow><mo>˜</mo></mrow></mover></math></span> is greater than one. Our results show that the intensity of white noise can affect the dynamical behaviors of the model. Finally, we use numerical simulation to illustrate theoretical results, and apply both the stochastic and deterministic models to analyze the outbreak of COVID-19 epidemic in Serbia.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110279"},"PeriodicalIF":0.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417136","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}
Pub Date : 2024-09-24DOI: 10.1016/j.spl.2024.110277
Hiroshi Saigo
The mean square error of the sample ratio under Lahiri’s design is derived and is compared with that under simple random sampling without replacement. New variance estimators of the sample ratio under the design are proposed. A simulation study is conducted to confirm the main results.
{"title":"Mean square error and variance estimation of the sample ratio under Lahiri ’s design","authors":"Hiroshi Saigo","doi":"10.1016/j.spl.2024.110277","DOIUrl":"10.1016/j.spl.2024.110277","url":null,"abstract":"<div><div>The mean square error of the sample ratio under Lahiri’s design is derived and is compared with that under simple random sampling without replacement. New variance estimators of the sample ratio under the design are proposed. A simulation study is conducted to confirm the main results.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110277"},"PeriodicalIF":0.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322756","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}
Pub Date : 2024-09-19DOI: 10.1016/j.spl.2024.110278
Sambit Panda , Cencheng Shen , Ronan Perry , Jelle Zorn , Antoine Lutz , Carey E. Priebe , Joshua T. Vogelstein
The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert–Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.
K 样本检验问题涉及确定 K 组数据点是否分别来自相同的分布。方差分析可以说是检验均值差异的最经典方法，最近还出现了几种检验分布差异的方法。在本文中，我们证明了一种转换的存在，它允许使用任何依赖性度量进行 K 样本检验。因此，普遍一致的 K 样本检验可以使用普遍一致的依赖性度量，如距离相关性和希尔伯特-施密特独立性准则。这样，各种依赖性测量方法就可以轻松地应用于 K 样本测试。
{"title":"Universally consistent K-sample tests via dependence measures","authors":"Sambit Panda , Cencheng Shen , Ronan Perry , Jelle Zorn , Antoine Lutz , Carey E. Priebe , Joshua T. Vogelstein","doi":"10.1016/j.spl.2024.110278","DOIUrl":"10.1016/j.spl.2024.110278","url":null,"abstract":"<div><div>The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert–Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110278"},"PeriodicalIF":0.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002475/pdfft?md5=8319efb92609b489dc9c39c93ef72fa6&pid=1-s2.0-S0167715224002475-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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