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A Basic Overview of Various Stochastic Approaches to Financial Modeling With Examples 附示例的各种财务建模随机方法基本概述
arXiv - MATH - History and Overview Pub Date : 2024-05-02 DOI: arxiv-2405.01397
Aashrit Cunchala
{"title":"A Basic Overview of Various Stochastic Approaches to Financial Modeling With Examples","authors":"Aashrit Cunchala","doi":"arxiv-2405.01397","DOIUrl":"https://doi.org/arxiv-2405.01397","url":null,"abstract":"This paper explores stochastic modeling approaches to elucidate the intricate\u0000dynamics of stock prices and volatility in financial markets. Beginning with an\u0000overview of Brownian motion and its historical significance in finance, we\u0000delve into various stochastic models, including the classic Black-Scholes\u0000framework, the Heston model, fractional Brownian motion, GARCH models, and Levy\u0000processes. Through a thorough investigation, we analyze the strengths and\u0000limitations of each model in capturing key features of financial time series\u0000data. Our empirical analysis focuses on parameter estimation and model\u0000calibration using Levy processes, demonstrating their effectiveness in\u0000predicting stock returns. However, we acknowledge the need for further\u0000refinement and exploration, suggesting potential avenues for future research,\u0000such as hybrid modeling approaches. Overall, this study underscores the\u0000importance of stochastic modeling in understanding market dynamics and informs\u0000decision-making in the financial industry.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140840749","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
Lovasz' Conjecture and Other Applications of Topological Methods in Discrete Mathematics 洛瓦兹猜想和离散数学中拓扑方法的其他应用
arXiv - MATH - History and Overview Pub Date : 2024-05-01 DOI: arxiv-2405.05273
Jingsi Hou, Guangyan Huang, Sammy Suliman, Haoran Yan
{"title":"Lovasz' Conjecture and Other Applications of Topological Methods in Discrete Mathematics","authors":"Jingsi Hou, Guangyan Huang, Sammy Suliman, Haoran Yan","doi":"arxiv-2405.05273","DOIUrl":"https://doi.org/arxiv-2405.05273","url":null,"abstract":"In 20th century mathematics, the field of topology, which concerns the\u0000properties of geometric objects under continuous transformation, has proved\u0000surprisingly useful in application to the study of discrete mathematics, such\u0000as combinatorics, graph theory, and theoretical computer science. In this\u0000paper, we seek to provide an introduction to the relevant topological concepts\u0000to non-specialists, as well as a selection of some existing applications to\u0000theorems in discrete mathematics.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926228","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
Report on the 50th Annual USA Mathematical Olympiad 第 50 届美国数学奥林匹克年会报告
arXiv - MATH - History and Overview Pub Date : 2024-04-28 DOI: arxiv-2406.09518
Bela Bajnok
{"title":"Report on the 50th Annual USA Mathematical Olympiad","authors":"Bela Bajnok","doi":"arxiv-2406.09518","DOIUrl":"https://doi.org/arxiv-2406.09518","url":null,"abstract":"We present the problems and solutions to the 50th Annual USA Mathematical\u0000Olympiad.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528414","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
Report on the 12th Annual USA Junior Mathematical Olympiad 第 12 届美国青少年数学奥林匹克年会报告
arXiv - MATH - History and Overview Pub Date : 2024-04-28 DOI: arxiv-2406.11094
Bela Bajnok, Evan Chen
{"title":"Report on the 12th Annual USA Junior Mathematical Olympiad","authors":"Bela Bajnok, Evan Chen","doi":"arxiv-2406.11094","DOIUrl":"https://doi.org/arxiv-2406.11094","url":null,"abstract":"We present the problems and solutions to the 12th Annual USA Junior\u0000Mathematical Olympiad.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"144 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528415","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
Report on the 61st Annual International Mathematical Olympiad 第 61 届国际数学奥林匹克年会报告
arXiv - MATH - History and Overview Pub Date : 2024-04-28 DOI: arxiv-2406.09517
Bela Bajnok, Evan Chen
{"title":"Report on the 61st Annual International Mathematical Olympiad","authors":"Bela Bajnok, Evan Chen","doi":"arxiv-2406.09517","DOIUrl":"https://doi.org/arxiv-2406.09517","url":null,"abstract":"We present the problems and solutions to the 61st Annual International\u0000Mathematical Olympiad","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528411","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
Algorithmic methods of finite discrete structures. The Four Color Theorem. Theory, methods, algorithms 有限离散结构的算法。四色定理。理论、方法、算法
arXiv - MATH - History and Overview Pub Date : 2024-04-26 DOI: arxiv-2405.05270
Sergey Kurapov, Maxim Davidovsky
{"title":"Algorithmic methods of finite discrete structures. The Four Color Theorem. Theory, methods, algorithms","authors":"Sergey Kurapov, Maxim Davidovsky","doi":"arxiv-2405.05270","DOIUrl":"https://doi.org/arxiv-2405.05270","url":null,"abstract":"The Four color problem is closely related to other branches of mathematics\u0000and practical applications. More than 20 of its reformulations are known, which\u0000connect this problem with problems of algebra, statistical mechanics and\u0000planning. And this is also typical for mathematics: the solution to a problem\u0000studied out of pure curiosity turns out to be useful in representing real\u0000objects and processes that are completely different in nature. Despite the\u0000published machine methods for combinatorial proof of the Four color conjecture,\u0000there is still no clear description of the mechanism for coloring a planar\u0000graph with four colors, its natural essence and its connection with the\u0000phenomenon of graph planarity. It is necessary not only to prove (preferably by\u0000deductive methods) that any planar graph can be colored with four colors, but\u0000also to show how to color it. The paper considers an approach based on the\u0000possibility of reducing a maximally flat graph to a regular flat cubic graph\u0000with its further coloring. Based on the Tate-Volynsky theorem, the vertices of\u0000a maximally flat graph can be colored with four colors, if the edges of its\u0000dual cubic graph can be colored with three colors. Considering the properties\u0000of a colored cubic graph, it can be shown that the addition of colors obeys the\u0000transformation laws of the fourth order Klein group. Using this property, it is\u0000possible to create algorithms for coloring planar graphs.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"186 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926429","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
Denoising: from classical methods to deep CNNs 去噪：从经典方法到深度 CNN
arXiv - MATH - History and Overview Pub Date : 2024-04-25 DOI: arxiv-2404.16617
Jean-Eric Campagne
{"title":"Denoising: from classical methods to deep CNNs","authors":"Jean-Eric Campagne","doi":"arxiv-2404.16617","DOIUrl":"https://doi.org/arxiv-2404.16617","url":null,"abstract":"This paper aims to explore the evolution of image denoising in a\u0000pedagological way. We briefly review classical methods such as Fourier analysis\u0000and wavelet bases, highlighting the challenges they faced until the emergence\u0000of neural networks, notably the U-Net, in the 2010s. The remarkable performance\u0000of these networks has been demonstrated in studies such as Kadkhodaie et al.\u0000(2024). They exhibit adaptability to various image types, including those with\u0000fixed regularity, facial images, and bedroom scenes, achieving optimal results\u0000and biased towards geometry-adaptive harmonic basis. The introduction of score\u0000diffusion has played a crucial role in image generation. In this context,\u0000denoising becomes essential as it facilitates the estimation of probability\u0000density scores. We discuss the prerequisites for genuine learning of\u0000probability densities, offering insights that extend from mathematical research\u0000to the implications of universal structures.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803601","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 mathematical work of Anania Shirakatsi 阿纳尼亚-希拉卡兹的数学工作
arXiv - MATH - History and Overview Pub Date : 2024-04-24 DOI: arxiv-2404.15945
Vahagn Aslanyan
{"title":"The mathematical work of Anania Shirakatsi","authors":"Vahagn Aslanyan","doi":"arxiv-2404.15945","DOIUrl":"https://doi.org/arxiv-2404.15945","url":null,"abstract":"This paper aims to give a brief account of the mathematical work of the\u00007th-century Armenian polymath and natural philosopher Anania Shirakatsi. The\u0000three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic\u0000operations, a list of problems and their answers, and a collection of\u0000entertaining puzzles -- are presented and discussed, the focus being on the\u0000problems and solutions. A close examination of the structure of these problems\u0000reveals that Anania's proficiency in arithmetic was considerably more\u0000sophisticated than their mathematical contents might suggest. The geography of\u0000Anania's problems is illustrated through two maps highlighting the locations\u0000referenced within these problems.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803600","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 AMC -- What It Is and Why It Matters AMC -- 它是什么，为什么重要
arXiv - MATH - History and Overview Pub Date : 2024-04-23 DOI: arxiv-2404.15511
Bela Bajnok
{"title":"The AMC -- What It Is and Why It Matters","authors":"Bela Bajnok","doi":"arxiv-2404.15511","DOIUrl":"https://doi.org/arxiv-2404.15511","url":null,"abstract":"A brief overview and history of the American Mathematics Competitions.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803656","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
Dominic Welsh (1938-2023) 多米尼克-威尔士（1938-2023）
arXiv - MATH - History and Overview Pub Date : 2024-04-22 DOI: arxiv-2404.13942
Geoffrey R. Grimmett
{"title":"Dominic Welsh (1938-2023)","authors":"Geoffrey R. Grimmett","doi":"arxiv-2404.13942","DOIUrl":"https://doi.org/arxiv-2404.13942","url":null,"abstract":"This biographical and scientific memoir of Dominic Welsh includes summaries\u0000of his important contributions to probability and combinatorics. With John\u0000Hammersley, he introduced first-passage percolation, and in so doing they\u0000formulated and proved the first subadditive ergodic theorem. Welsh has numerous\u0000results in matroid theory, and wrote the first monograph on the topic. He\u0000worked on computational complexity and particularly the complexity of computing\u0000the Tutte polynomial. He was an inspirational teacher and advisor who helped to\u0000develop a community of scholars in combinatorics.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803715","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
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