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Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation 具有跳跃的时滞ait - sahalia型利率模型及其强逼近
IF 1.5
Statistics & Risk Modeling Pub Date : 2023-08-25 DOI: 10.1515/strm-2022-0013
E. Coffie
{"title":"Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation","authors":"E. Coffie","doi":"10.1515/strm-2022-0013","DOIUrl":"https://doi.org/10.1515/strm-2022-0013","url":null,"abstract":"Abstract In this paper, we study the analytical properties of the true solution to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jumps. Since this model does not have a closed-form solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate the finite-time strong convergence theory of the numerical solution under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43664596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minkowski deviation measures 闵可夫斯基偏差测量
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-12-09 DOI: 10.1515/strm-2021-0033
Marlon Moresco, Marcelo Brutti Righi, E. Horta
{"title":"Minkowski deviation measures","authors":"Marlon Moresco, Marcelo Brutti Righi, E. Horta","doi":"10.1515/strm-2021-0033","DOIUrl":"https://doi.org/10.1515/strm-2021-0033","url":null,"abstract":"Abstract We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink or deleverage a financial position for it to become acceptable. In particular, the Minkowski Deviation of a set which is convex, translation insensitive, and radially bounded at non-constants, is a generalized deviation measure in the sense of [R. T. Rockafellar, S. Uryasev and M. Zabarankin, Generalized deviations in risk analysis, Finance Stoch. 10 2006, 1, 51–74]. Furthermore, we explore the converse relations from properties of a Minkowski Deviation to its sub-level sets, introducing the notion of acceptance sets for deviations. Hence, we fill a gap existing in the literature, namely the lack of a well-defined concept of acceptance sets for deviation measures. Dual characterizations in terms of polar sets and support functionals are provided.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47013827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A robust estimator of the proportional hazard transform for massive data 大数据比例风险变换的鲁棒估计
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-10-14 DOI: 10.1515/strm-2020-0007
Tami Omar, Rassoul Abdelaziz, Ould Rouis Hamid
{"title":"A robust estimator of the proportional hazard transform for massive data","authors":"Tami Omar, Rassoul Abdelaziz, Ould Rouis Hamid","doi":"10.1515/strm-2020-0007","DOIUrl":"https://doi.org/10.1515/strm-2020-0007","url":null,"abstract":"Abstract In this paper, we explore the idea of grouping under the massive data framework, to propose a median-of-means non-parametric type estimator for the Proportional Hazard Transform (PHT), which has been widely used in finance and insurance. Under certain conditions on the growth rate of subgroups, the consistency and asymptotic normality of the proposed estimators are investigated. Furthermore, we construct a new method to test PHT based on the empirical likelihood method for the median in order to avoid any prior estimate of the variance structure for the proposed estimator, as it is difficult to estimate and often causes much inaccuracy. Numerical simulations and real-data analysis are designed to show the present estimator’s performance. The results confirm that the new put-forward estimator is quite robust with respect to outliers.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49155229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic properties of duration-based VaR backtests 基于持续时间的VaR回溯检验的渐近性质
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-07-01 DOI: 10.1515/strm-2021-0019
Marta Małecka
{"title":"Asymptotic properties of duration-based VaR backtests","authors":"Marta Małecka","doi":"10.1515/strm-2021-0019","DOIUrl":"https://doi.org/10.1515/strm-2021-0019","url":null,"abstract":"Abstract To increase the power of the VaR tests, it has been recently proposed to extend the duration-based test class with the geometric-VaR and Gini-coefficient-based tests. These tests, though exhibiting outstanding power properties, have not gained recognition in the industry. A potential reason is the absence of ready-to-use statistical distributions. To remedy this, we inquire into the limiting properties of these tests and derive relevant asymptotic distributions. We also provide a generalized geometric-VaR test and give its distribution. Through the Monte Carlo study, we show the accuracy of our asymptotic procedures in finite samples, and we find these procedures to be relevant for the current Basel standards. Our theoretical results are illustrated by the empirical study that includes data from the current COVID-19 crisis.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Penalised likelihood methods for phase-type dimension selection 相型维数选择的惩罚似然法
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-07-01 DOI: 10.1515/strm-2021-0026
H. Albrecher, Martin Bladt, Alaric J. A. Müller
{"title":"Penalised likelihood methods for phase-type dimension selection","authors":"H. Albrecher, Martin Bladt, Alaric J. A. Müller","doi":"10.1515/strm-2021-0026","DOIUrl":"https://doi.org/10.1515/strm-2021-0026","url":null,"abstract":"Abstract Phase-type distributions are dense in the class of distributions on the positive real line, and their flexibility and closed-form formulas in terms of matrix calculus allow fitting models to data in various application areas. However, the parameters are in general non-identifiable, and hence the dimension of two similar models may be very different. This paper proposes a new method for selecting the dimension of phase-type distributions via penalisation of the likelihood function. The penalties are in terms of the Green matrix, from which it is possible to extract the contributions of each state to the overall mean. Since representations with higher dimensions are penalised, a parsimony effect is obtained. We perform a numerical study with randomly generated phase-type samples to illustrate the effectiveness of the proposed procedure, and also apply the technique to the absolute log-returns of EURO STOXX 50 and Bitcoin prices.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42230889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Systemic risk models for disjoint and overlapping groups with equilibrium strategies 具有均衡策略的不相交和重叠群体的系统风险模型
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-02-01 DOI: 10.1515/strm-2022-0004
Yichen Feng, J. Fouque, Ruimeng Hu, Tomoyuki Ichiba
{"title":"Systemic risk models for disjoint and overlapping groups with equilibrium strategies","authors":"Yichen Feng, J. Fouque, Ruimeng Hu, Tomoyuki Ichiba","doi":"10.1515/strm-2022-0004","DOIUrl":"https://doi.org/10.1515/strm-2022-0004","url":null,"abstract":"Abstract We analyze the systemic risk for disjoint and overlapping groups of financial institutions by proposing new models with realistic game features. Specifically, we generalize the systemic risk measure proposed in [F. Biagini, J.-P. Fouque, M. Frittelli and T. Meyer-Brandis, On fairness of systemic risk measures, Finance Stoch. 24 (2020), 2, 513–564] by allowing individual banks to choose their preferred groups instead of being assigned to certain groups. We introduce the concept of Nash equilibrium for these new models, and analyze the optimal solution under Gaussian distribution of the risk factor. We also provide an explicit solution for the risk allocation of the individual banks and study the existence and uniqueness of Nash equilibrium both theoretically and numerically. The developed numerical algorithm can simulate scenarios of equilibrium, and we apply it to study the banking structure with real data and show the validity of the proposed model.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45250405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Multi-component stress-strength model for Weibull distribution in progressively censored samples 渐进式截尾样本威布尔分布的多分量应力-强度模型
IF 1.5
Statistics & Risk Modeling Pub Date : 2022-01-01 DOI: 10.1515/strm-2020-0030
A. Kohansal, S. Shoaee, S. Nadarajah
{"title":"Multi-component stress-strength model for Weibull distribution in progressively censored samples","authors":"A. Kohansal, S. Shoaee, S. Nadarajah","doi":"10.1515/strm-2020-0030","DOIUrl":"https://doi.org/10.1515/strm-2020-0030","url":null,"abstract":"Abstract One of the important issues is risk assessment and calculation in complex and multi-component systems. In this paper, the estimation of multi-component stress-strength reliability for the Weibull distribution under the progressive Type-II censored samples is studied. We assume that both stress and strength are two independent Weibull distributions with different parameters. First, assuming the same shape parameter, the maximum likelihood estimation (MLE), different approximations of Bayes estimators (Lindley’s approximation and Markov chain Monte Carlo method) and different confidence intervals (asymptotic and highest posterior density) are obtained. In the case when the shape parameter is known, the MLE, uniformly minimum variance unbiased estimator (UMVUE), exact Bayes estimator and different confidence intervals (asymptotic and highest posterior density) are considered. Finally, in the general case, the statistical inferences on multi-component stress-strength reliability are derived. To compare the performances of different methods, Monte Carlo simulations are performed. Moreover, one data set for illustrative purposes is analyzed.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46185321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Kernel estimation for Lévy driven stochastic convolutions lsamvy驱动随机卷积的核估计
IF 1.5
Statistics & Risk Modeling Pub Date : 2021-08-11 DOI: 10.1515/strm-2021-0007
F. Comte, V. Genon-Catalot
{"title":"Kernel estimation for Lévy driven stochastic convolutions","authors":"F. Comte, V. Genon-Catalot","doi":"10.1515/strm-2021-0007","DOIUrl":"https://doi.org/10.1515/strm-2021-0007","url":null,"abstract":"Abstract We consider a Lévy driven stochastic convolution, also called continuous time Lévy driven moving average model X⁢(t)=∫0ta⁢(t-s)⁢dZ⁢(s)X(t)=int_{0}^{t}a(t-s),dZ(s), where 𝑍 is a Lévy martingale and the kernel a(.)a(,{.},) a deterministic function square integrable on R+mathbb{R}^{+}. Given 𝑁 i.i.d. continuous time observations (Xi⁢(t))t∈[0,T](X_{i}(t))_{tin[0,T]}, i=1,…,Ni=1,dots,N, distributed like (X⁢(t))t∈[0,T](X(t))_{tin[0,T]}, we propose two types of nonparametric projection estimators of a2a^{2} under different sets of assumptions. We bound the L2mathbb{L}^{2}-risk of the estimators and propose a data driven procedure to select the dimension of the projection space, illustrated by a short simulation study.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44550903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The functional kNN estimator of the conditional expectile: Uniform consistency in number of neighbors 条件期望的函数kNN估计量：邻域数的一致一致性
IF 1.5
Statistics & Risk Modeling Pub Date : 2021-07-01 DOI: 10.1515/strm-2019-0029
I. Almanjahie, S. Bouzebda, Zouaoui Chikr Elmezouar, Ali Laksaci
{"title":"The functional kNN estimator of the conditional expectile: Uniform consistency in number of neighbors","authors":"I. Almanjahie, S. Bouzebda, Zouaoui Chikr Elmezouar, Ali Laksaci","doi":"10.1515/strm-2019-0029","DOIUrl":"https://doi.org/10.1515/strm-2019-0029","url":null,"abstract":"Abstract The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors (UNN) of the constructed estimator. The usefulness of our result for the smoothing parameter automatic selection is discussed. Short simulation results show that the finite sample performance of the proposed estimator is satisfactory in moderate sample sizes. We finally examine the implementation of this model in practice with a real data in financial risk analysis.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43495581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Bipolar behavior of submodular, law-invariant capacities 子模、律不变容量的双极行为
IF 1.5
Statistics & Risk Modeling Pub Date : 2021-07-01 DOI: 10.1515/strm-2020-0025
M. Amarante
{"title":"Bipolar behavior of submodular, law-invariant capacities","authors":"M. Amarante","doi":"10.1515/strm-2020-0025","DOIUrl":"https://doi.org/10.1515/strm-2020-0025","url":null,"abstract":"Abstract In the case of a submodular, law-invariant capacity, we provide an entirely elementary proof of a result of Marinacci [M. Marinacci, Upper probabilities and additivity, Sankhyā Ser. A 61 1999, no. 3, 358–361]. As a corollary, we also show that the anticore of a continuous submodular, law-invariant nonatomic capacity has a dichotomous nature: either it is one-dimensional or it is infinite-dimensional. The results have implications for the use of such capacities in financial and economic applications.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42086447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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