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International Journal of Stochastic Analysis最新文献

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Optimal Foreign Exchange Rate Intervention in Lévy Markets 汇兑市场的最优汇率干预
International Journal of Stochastic Analysis Pub Date : 2014-11-26 DOI: 10.1155/2014/746815
Masimba Aspinas Mutakaya, Eriyoti Chikodza, Edward T. Chiyaka
{"title":"Optimal Foreign Exchange Rate Intervention in Lévy Markets","authors":"Masimba Aspinas Mutakaya, Eriyoti Chikodza, Edward T. Chiyaka","doi":"10.1155/2014/746815","DOIUrl":"https://doi.org/10.1155/2014/746815","url":null,"abstract":"This paper considers an exchange rate problem in Levy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value. The interventions by the Central Bank are associated with costs. We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends the model by Huang, 2009, to incorporate a jump component. We formulate and prove an optimal verification theorem for the impulse control. We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121557386","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
A Note on the Distribution of Multivariate Brownian Extrema 关于多元布朗极值分布的注记
International Journal of Stochastic Analysis Pub Date : 2014-11-16 DOI: 10.1155/2014/575270
M. Escobar, J. Hernández
{"title":"A Note on the Distribution of Multivariate Brownian Extrema","authors":"M. Escobar, J. Hernández","doi":"10.1155/2014/575270","DOIUrl":"https://doi.org/10.1155/2014/575270","url":null,"abstract":"This paper presents a closed-form solution for the joint probability of the endpoints and minimums of a multidimensional Wiener process for some correlation matrices. This is the only explicit expressions found in the literature for this joint probability. The analysis can only be carried out for special correlation structures as it is related to the fundamentals regions of irreducible spherical simplexes generated by \u0000reflections and the link to the method of images. This joint distribution can be used in financial mathematics to obtain prices of credit or market related products in high dimension. The solution could be generalized to account for stochastic volatility and other stylized features of the financial markets.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124973950","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
A Discrete-Time Queue with Balking, Reneging, and Working Vacations 一个离散时间队列与犹豫，食言，和工作假期
International Journal of Stochastic Analysis Pub Date : 2014-10-29 DOI: 10.1155/2014/358529
V. Goswami
{"title":"A Discrete-Time Queue with Balking, Reneging, and Working Vacations","authors":"V. Goswami","doi":"10.1155/2014/358529","DOIUrl":"https://doi.org/10.1155/2014/358529","url":null,"abstract":"This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129403921","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: 16
Limit Properties of Transition Functions of Continuous-Time Markov Branching Processes 连续时间马尔可夫分支过程转移函数的极限性质
International Journal of Stochastic Analysis Pub Date : 2014-10-19 DOI: 10.1155/2014/409345
A. Imomov
{"title":"Limit Properties of Transition Functions of Continuous-Time Markov Branching Processes","authors":"A. Imomov","doi":"10.1155/2014/409345","DOIUrl":"https://doi.org/10.1155/2014/409345","url":null,"abstract":"Consider the Markov Branching Process with continuous time. Our focus is on the limit properties of transition functions of this process. Using differential analogue of the Basic Lemma we prove local limit theorems for all cases and observe invariant properties of considering process.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116368689","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
Stochastic Analysis of Gaussian Processes via Fredholm Representation 基于Fredholm表示的高斯过程随机分析
International Journal of Stochastic Analysis Pub Date : 2014-10-08 DOI: 10.1155/2016/8694365
T. Sottinen, L. Viitasaari
{"title":"Stochastic Analysis of Gaussian Processes via Fredholm Representation","authors":"T. Sottinen, L. Viitasaari","doi":"10.1155/2016/8694365","DOIUrl":"https://doi.org/10.1155/2016/8694365","url":null,"abstract":"We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"20 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122839581","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: 30
Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems 对冲、期权定价和保险问题的倒向随机微分方程方法
International Journal of Stochastic Analysis Pub Date : 2014-09-11 DOI: 10.1155/2014/152389
F. Cordoni, L. Persio
{"title":"Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems","authors":"F. Cordoni, L. Persio","doi":"10.1155/2014/152389","DOIUrl":"https://doi.org/10.1155/2014/152389","url":null,"abstract":"In the present work we give a self-contained introduction to financial mathematical models characterized by noise of Levy type in the framework of the backward stochastic differential equations theory. Such techniques will be then used to analyse an innovative model related to insurance and death processes setting.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128312841","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: 20
Generalisation of Hajek’s Stochastic Comparison Results to Stochastic Sums Hajek随机比较结果在随机和中的推广
International Journal of Stochastic Analysis Pub Date : 2014-08-13 DOI: 10.1155/2016/1018509
J. Kampen
{"title":"Generalisation of Hajek’s Stochastic Comparison Results to Stochastic Sums","authors":"J. Kampen","doi":"10.1155/2016/1018509","DOIUrl":"https://doi.org/10.1155/2016/1018509","url":null,"abstract":"Hajek’s univariate stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monotonic nondecreasing convex data functions for processes with and without drift, respectively. As a consequence strategies for a class of multivariate optimal control problems can be determined by maximizing variance. An example is passport options written on multivariate traded accounts. The argument describes a narrow path between impossibilities of generalisations to jump processes or impossibilities of more general data functions.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"20 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115000953","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
Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity 具有加性噪声和时间奇点的随机微分方程强解的有效变步长逼近
International Journal of Stochastic Analysis Pub Date : 2014-07-02 DOI: 10.1155/2014/852962
H. Hughes, Pathiranage Lochana Siriwardena
{"title":"Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity","authors":"H. Hughes, Pathiranage Lochana Siriwardena","doi":"10.1155/2014/852962","DOIUrl":"https://doi.org/10.1155/2014/852962","url":null,"abstract":"We consider stochastic differential equations with additive noise and conditions on the coefficients in those equations that allow a time singularity in the drift coefficient. Given a maximum step size, , we specify variable (adaptive) step sizes relative to which decrease as the time node points approach the singularity. We use an Euler-type numerical scheme to produce an approximate solution and estimate the error in the approximation. When the solution is restricted to a fixed closed time interval excluding the singularity, we obtain a global pointwise error of order . An order of error for any is obtained when the approximation is run up to a time within of the singularity for an appropriate choice of exponent . We apply this scheme to Brownian bridge, which is defined as the nonanticipating solution of a stochastic differential equation of the type under consideration. In this special case, we show that the global pointwise error is of order , independent of how close to the singularity the approximation is considered.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126535322","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 Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet 全资产负债表的双模平均场最优切换问题
International Journal of Stochastic Analysis Pub Date : 2014-05-25 DOI: 10.1155/2014/159519
Boualem Djehiche, Ali Hamdi
{"title":"A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet","authors":"Boualem Djehiche, Ali Hamdi","doi":"10.1155/2014/159519","DOIUrl":"https://doi.org/10.1155/2014/159519","url":null,"abstract":"We consider the problem of switching a large number of production lines between two modes, high production and low production. The switching is based on the optimal expected profit and cost yields of the respective production lines and considers both sides of the balance sheet. Furthermore, the production lines are all assumed to be interconnected through a coupling term, which is the average of all optimal expected yields. Intuitively, this means that each individual production line is compared to the average of all its peers which acts as a benchmark. Due to the complexity of the problem, we consider the aggregated optimal expected yields, where the coupling term is approximated with the mean of the optimal expected yields. This turns the problem into a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125465253","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
Large Deviation Analysis of a Droplet Model Having a Poisson Equilibrium Distribution 具有泊松平衡分布的液滴模型的大偏差分析
International Journal of Stochastic Analysis Pub Date : 2014-05-20 DOI: 10.1155/2015/287450
R. Ellis, S. Ta'asan
{"title":"Large Deviation Analysis of a Droplet Model Having a Poisson Equilibrium Distribution","authors":"R. Ellis, S. Ta'asan","doi":"10.1155/2015/287450","DOIUrl":"https://doi.org/10.1155/2015/287450","url":null,"abstract":"In this paper we use large deviation theory to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and statistical mechanics. Given and , distinguishable particles are placed, each with equal probability , onto the sites of a lattice, where equals . We focus on configurations for which each site is occupied by a minimum of particles. The main result is the large deviation principle (LDP), in the limit and with , for a sequence of random, number-density measures, which are the empirical measures of dependent random variables that count the droplet sizes. The rate function in the LDP is the relative entropy , where is a possible asymptotic configuration of the number-density measures and is a Poisson distribution with mean , restricted to the set of positive integers satisfying . This LDP implies that is the equilibrium distribution of the number-density measures, which in turn implies that is the equilibrium distribution of the random variables that count the droplet sizes.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132932585","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
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