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ON OPTIMAL THRESHOLDS FOR PAIRS TRADING IN A ONE-DIMENSIONAL DIFFUSION MODEL 一维扩散模型中配对交易的最优阈值
The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000298
M. Fukasawa, Hitomi Maeda, J. Sekine
{"title":"ON OPTIMAL THRESHOLDS FOR PAIRS TRADING IN A ONE-DIMENSIONAL DIFFUSION MODEL","authors":"M. Fukasawa, Hitomi Maeda, J. Sekine","doi":"10.1017/S1446181121000298","DOIUrl":"https://doi.org/10.1017/S1446181121000298","url":null,"abstract":"Abstract We study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic arbitrage in the long run of the threshold strategy is observed.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"3 1","pages":"104 - 122"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74247236","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 REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS 单相heli - shaw流及其非标准结构的水平集方法综述
The ANZIAM journal Pub Date : 2021-01-19 DOI: 10.1017/S144618112100033X
Liam C. Morrow, T. Moroney, M. Dallaston, S. McCue
{"title":"A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS","authors":"Liam C. Morrow, T. Moroney, M. Dallaston, S. McCue","doi":"10.1017/S144618112100033X","DOIUrl":"https://doi.org/10.1017/S144618112100033X","url":null,"abstract":"Abstract The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman–Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical scheme for studying both the standard and nonstandard Hele-Shaw flows. Our method consists of using a modified finite-difference stencil in conjunction with the level-set method to solve the governing equation for pressure on complicated domains and track the location of the moving boundary. Simulations show that our method is capable of reproducing the distinctive morphological features of the Saffman–Taylor instability on a uniform computational grid. By making straightforward adjustments, we show how our scheme can easily be adapted to solve for a wide variety of nonstandard configurations, including cases where the gap between the plates is linearly tapered, the plates are separated in time, and the entire Hele-Shaw cell is rotated at a given angular velocity.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"30 1","pages":"269 - 307"},"PeriodicalIF":0.0,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87449969","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: 10
ANZ VOLUME 63 ISSUE 1 COVER AND FRONT MATTER 澳新银行第63卷第1期封面和封面
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/s1446181121000134
{"title":"ANZ VOLUME 63 ISSUE 1 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181121000134","DOIUrl":"https://doi.org/10.1017/s1446181121000134","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"68 1","pages":"f1 - f2"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84592336","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
ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH 呈指数增长的不对称细胞分裂
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000109
A. Zaidi, B. VAN BRUNT
{"title":"ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH","authors":"A. Zaidi, B. VAN BRUNT","doi":"10.1017/S1446181121000109","DOIUrl":"https://doi.org/10.1017/S1446181121000109","url":null,"abstract":"Abstract An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield nontrivial solutions to the problem for certain choices of growth and division rates of cells. We also consider the asymmetric division of cells with linear growth rate which corresponds to “exponential growth” and exponential rate of cell division, and show that the solution to the problem is a certain Dirichlet series. The distribution of the first moment of the biomass is shown to be unimodal.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"13 1","pages":"70 - 83"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80646831","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
ANZ VOLUME 63 ISSUE 1 COVER AND BACK MATTER 澳新银行第63卷第1期封面和封底
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/s1446181121000146
{"title":"ANZ VOLUME 63 ISSUE 1 COVER AND BACK MATTER","authors":"","doi":"10.1017/s1446181121000146","DOIUrl":"https://doi.org/10.1017/s1446181121000146","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"5 1","pages":"b1 - b6"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80900445","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
STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH 基于分布鲁棒优化的航天器交会对接随机模型预测控制
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000031
Zuoxun Li, Kai Zhang
{"title":"STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH","authors":"Zuoxun Li, Kai Zhang","doi":"10.1017/S1446181121000031","DOIUrl":"https://doi.org/10.1017/S1446181121000031","url":null,"abstract":"Abstract A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"97 1","pages":"39 - 57"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81616384","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
ANALYSIS OF CELL TRANSMISSION MODEL FOR TRAFFIC FLOW SIMULATION WITH APPLICATION TO NETWORK TRAFFIC 交通流仿真的小区传输模型分析及其在网络交通中的应用
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000080
A. Maulana, S. R. Pudjaprasetya
{"title":"ANALYSIS OF CELL TRANSMISSION MODEL FOR TRAFFIC FLOW SIMULATION WITH APPLICATION TO NETWORK TRAFFIC","authors":"A. Maulana, S. R. Pudjaprasetya","doi":"10.1017/S1446181121000080","DOIUrl":"https://doi.org/10.1017/S1446181121000080","url":null,"abstract":"Abstract The cell transmission model (CTM) is a macroscopic model that describes the dynamics of traffic flow over time and space. The effectiveness and accuracy of the CTM are discussed in this paper. First, the CTM formula is recognized as a finite-volume discretization of the kinematic traffic model with a trapezoidal flux function. To validate the constructed scheme, the simulation of shock waves and rarefaction waves as two important elements of traffic dynamics was performed. Adaptation of the CTM for intersecting and splitting cells is discussed. Its implementation on the road segment with traffic influx produces results that are consistent with the analytical solution of the kinematic model. Furthermore, a simulation on a simple road network shows the back and forth propagation of shock waves and rarefaction waves. Our numerical result agrees well with the existing result of Godunov’s finite-volume scheme. In addition, from this accurately proven scheme, we can extract information for the average travel time on a certain route, which is the most important information a traveller needs. It appears from simulations of different scenarios that, depending on the circumstances, a longer route may have a shorter travel time. Finally, there is a discussion on the possible application for traffic management in Indonesia during the Eid al-Fitr exodus.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"1 1","pages":"84 - 99"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72618178","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
SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING dufort-frankel有限差分的缓燃不稳定性
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000043
D. Galloway, D. Ivers
{"title":"SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING","authors":"D. Galloway, D. Ivers","doi":"10.1017/S1446181121000043","DOIUrl":"https://doi.org/10.1017/S1446181121000043","url":null,"abstract":"Abstract DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"167 1","pages":"23 - 38"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82611811","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
ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS 具有小陷阱簇的有限周期或空间周期二维区域的平均首次通过时间的渐近分析
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000018
S. Iyaniwura, M. Ward
{"title":"ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS","authors":"S. Iyaniwura, M. Ward","doi":"10.1017/S1446181121000018","DOIUrl":"https://doi.org/10.1017/S1446181121000018","url":null,"abstract":"Abstract A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as “traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"108 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73422290","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: 6
EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS 火焰锋面无坐标模型的高效计算
The ANZIAM journal Pub Date : 2021-01-01 DOI: 10.1017/S1446181121000079
B. Akers, D. Ambrose
{"title":"EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS","authors":"B. Akers, D. Ambrose","doi":"10.1017/S1446181121000079","DOIUrl":"https://doi.org/10.1017/S1446181121000079","url":null,"abstract":"Abstract We present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff, highly accurate solver which can handle fully nonlinear, overturned interfaces, with similar computational expense to methods for weakly nonlinear models. We apply this solver both to simulate overturned flame fronts and to compare the accuracy of Kuramoto–Sivashinsky and coordinate-free models in the appropriate limit.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"4 1","pages":"58 - 69"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78509191","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: 6
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