L\'evy processes optimal stopping problems and stochastic games

Levy 处理最优停止问题和随机博弈

基本信息

  • 批准号:
    EP/D045460/1
  • 负责人:
  • 金额:
    $ 18.48万
  • 依托单位:
  • 依托单位国家:
    英国
  • 项目类别:
    Research Grant
  • 财政年份:
    2007
  • 资助国家:
    英国
  • 起止时间:
    2007 至 无数据
  • 项目状态:
    已结题

项目摘要

Levy processes may be thought of as a class of models that describe the motion or path of a randomly moving particle which may diffuse or undergo independent random jumps whose order of magnitude may be both arbitrarily large or arbitrarily small. Levy processes have several distributional properties built in to their random structure that make them particularly attractive to work with as a mathematical tool when building and analyzing certain themes from within the field of applied probability. One such theme forms the focus of this proposal; optimal stopping and stochastic games.Optimal stopping problems are a class of mathematical problems in which a player may stop a randomly moving process, such as a Levy process, in order to claim a prize equal in value to some prespecified function of the random process at the time of stopping. A fundamental problem is to establish an optmimal stopping strategy according to some optimization criteria.Stochastic games are a variant on this theme in which two players may stop a randomly moving process. The consequence of their actions is that, whoever stops first, player 1 will receive a prespecified function of the random process at the time of stopping which is to be paid for by player 2. The prespecified function used depends only on who has stopped first. A fundamental problem here is to establish stopping strategies for both players according to sensible optimization criteria. Typically player 1 will want to gain as much wealth as possible whilst player 2 will want to reduce the value of their obligation as much as possible.This project deals with a number of mathematical phenomena which appear in such problems when the underlying randomly moving process is a Levy process. There is very little known about explicit solutions to such problems in the existing literature. Many mathematical difficulties arise becasue of the way in which Levy processes jump along their trajectory. None the less there is now a sufficiently well developed theory of Levy processes in order to look at its application in this context.In many cases, it is possible to express the pricing of exotic options in financial markets as the solution to either an optimal stopping problem or a stochastic game. With the recent preference for the use of Levy processes as an underlying source of randomness in market models, the current proposal is very timely and will be of direct interest within the field of financial mathematics.
列维过程可以被认为是一类描述随机运动粒子的运动或路径的模型,这些粒子可以扩散或经历独立的随机跳跃,其数量级可以是任意大或任意小。利维过程有几个分布特性内置于其随机结构中,这使得它们在构建和分析应用概率领域的某些主题时作为数学工具特别有吸引力。最优停止问题(optimal stopping problem)是一类数学问题,在这类问题中,一个参与者可以停止一个随机运动的过程,例如一个Levy过程,以获得一个与停止时随机过程的某个预先指定的函数相等的奖励。一个基本的问题是建立一个最优的停止策略,根据一些优化准则。随机游戏是一个变种,在这个主题中,两个球员可以停止一个随机移动的过程。他们行动的结果是,无论谁先停止,参与人1将在停止时收到一个随机过程的预先指定的函数,该函数将由参与人2支付。所使用的预先指定的函数仅取决于谁先停止。这里的一个基本问题是根据合理的优化标准为两个玩家建立停止策略。通常情况下,玩家1会想获得尽可能多的财富,而玩家2会想尽可能减少他们的债务价值。这个项目涉及的数学现象出现在这样的问题时,潜在的随机移动过程是一个利维过程。在现有的文献中,很少有人知道这类问题的显式解。许多数学上的困难是由于列维过程沿其轨迹沿着跳跃的方式而产生的。尽管如此,现在已经有一个充分发展的Levy过程理论,以便研究它在这方面的应用,在许多情况下,可以将金融市场中奇异期权的定价表示为最优停止问题或随机博弈的解。最近倾向于使用Levy过程作为市场模型中随机性的潜在来源,目前的建议非常及时,将在金融数学领域内直接感兴趣。

项目成果

期刊论文数量(10)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Meromorphic Lévy processes and their fluctuation identities
亚形 Lévy 过程及其涨落特性
The Shepp-Shiryaev Stochastic Game Driven by a Spectrally Negative Lévy Process
由谱负 Lévy 过程驱动的 Shepp-Shiryaev 随机博弈
Explicit identities for Lévy processes associated to symmetric stable processes
与对称稳定过程相关的 Lévy 过程的显式恒等式
  • DOI:
    10.3150/10-bej275
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    1.5
  • 作者:
    Caballero M
  • 通讯作者:
    Caballero M
Fluctuation theory and exit systems for positive self-similar Markov processes
正自相似马尔可夫过程的波动理论和退出系统
  • DOI:
    10.48550/arxiv.0812.2506
  • 发表时间:
    2008
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Chaumont L
  • 通讯作者:
    Chaumont L
On the Lamperti stable processes
关于 Lamperti 稳定过程
  • DOI:
    10.48550/arxiv.0802.0851
  • 发表时间:
    2008
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Caballero M
  • 通讯作者:
    Caballero M
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Andreas Kyprianou其他文献

Small Airway Disease, Air Trapping and Airways Responsiveness in Patients With Primary Pulmonary Hypertensio
  • DOI:
    10.1378/chest.124.4_meetingabstracts.222s
  • 发表时间:
    2003-01-01
  • 期刊:
  • 影响因子:
  • 作者:
    Andreas Kyprianou;Darrin London;Maria Padilla;N. Kohn;Al Quinones;Steven Feinsilver;Alan Fein;X Arunabh
  • 通讯作者:
    X Arunabh
Extreme Supervised Algorithm for Day Ahead Market Price Forecasting
用于日前市场价格预测的极端监督算法
  • DOI:
    10.1109/isc257844.2023.10293566
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Stylianos Loizidis;S. Theocharides;V. Venizelou;Demetris Evagorou;G. Makrides;Andreas Kyprianou;G. Georghiou
  • 通讯作者:
    G. Georghiou
Utility of Centrifugation Lysis Blood Cultures in the Diagnosis of Mycobacteria Tuberculosis in HIV Patients: Association With CD4 Counts <50 cells/mm
  • DOI:
    10.1378/chest.124.4_meetingabstracts.114s-b
  • 发表时间:
    2003-01-01
  • 期刊:
  • 影响因子:
  • 作者:
    M. Desruisseaux;Andreas Kyprianou;M.H. Kaplan;A.M. Fein;X. Arunabh
  • 通讯作者:
    X. Arunabh
A stochastic optimisation framework for integrating photovoltaic systems, heat pumps, and energy storage in buildings
  • DOI:
    10.1016/j.applthermaleng.2025.127312
  • 发表时间:
    2025-11-01
  • 期刊:
  • 影响因子:
    6.900
  • 作者:
    Andreas V. Olympios;Matthias Mersch;Fanourios Kourougianni;Christos N. Markides;Antonio M. Pantaleo;Andreas Kyprianou;George E. Georghiou
  • 通讯作者:
    George E. Georghiou
Entrance laws at the origin of self-similar Markov processes in high dimensions
高维自相似马尔可夫过程起源的入口定律

Andreas Kyprianou的其他文献

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{{ truncateString('Andreas Kyprianou', 18)}}的其他基金

Random fragmentation-coalescence processes out of equilibrium
随机分裂-聚结过程失去平衡
  • 批准号:
    EP/S036202/2
  • 财政年份:
    2023
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Mathematical Theory of Radiation Transport: Nuclear Technology Frontiers (MaThRad)
辐射传输数学理论:核技术前沿(MaThRad)
  • 批准号:
    EP/W026899/2
  • 财政年份:
    2023
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Mathematical Theory of Radiation Transport: Nuclear Technology Frontiers (MaThRad)
辐射传输数学理论:核技术前沿(MaThRad)
  • 批准号:
    EP/W026899/1
  • 财政年份:
    2022
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Random fragmentation-coalescence processes out of equilibrium
随机分裂-聚结过程失去平衡
  • 批准号:
    EP/S036202/1
  • 财政年份:
    2020
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Stochastic analysis of the neutron transport equation and applications to nuclear safety
中子输运方程的随机分析及其在核安全中的应用
  • 批准号:
    EP/P009220/1
  • 财政年份:
    2017
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Real-valued self-similar Markov processes and their applications
实值自相似马尔可夫过程及其应用
  • 批准号:
    EP/L002442/1
  • 财政年份:
    2014
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Self-similarity and stable processes
自相似性和稳定过程
  • 批准号:
    EP/M001784/1
  • 财政年份:
    2014
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Analytical properties of scale functions
尺度函数的分析性质
  • 批准号:
    EP/E047025/1
  • 财政年份:
    2007
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant
Random walks and branching processes in random environments under Spitzer's condition
斯皮策条件下随机环境中的随机游走和分支过程
  • 批准号:
    EP/D064988/1
  • 财政年份:
    2006
  • 资助金额:
    $ 18.48万
  • 项目类别:
    Research Grant

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