Trajectorial Martingales and Worst Case Approach to Market Models

轨迹鞅和市场模型的最坏情况方法

基本信息

  • 批准号:
    RGPIN-2018-03867
  • 负责人:
  • 金额:
    $ 1.46万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2022
  • 资助国家:
    加拿大
  • 起止时间:
    2022-01-01 至 2023-12-31
  • 项目状态:
    已结题

项目摘要

Financial markets are an essential part of modern societies; they provide the needed capital to make a myriad of economical activities possible. Regrettably, the negative side of financial speculation as well as the availability of cheap and unlimited credit create undesirable side effects (e.g. market crashes, uncontrollable debt, etc). In short, there is a definite need for a better understanding of financial markets. Stochastic modeling in financial mathematics is presently being generalized to incorporate higher levels of uncertainty. This initiative reflects the current inability of models to incorporate all variables that affect market conditions as well as a reliable joint probability distribution. Along this modern line of research, we propose an approach that weakens dramatically basic stochastic modeling assumptions. Conclusions in such an approach are more robust as they are less dependent on prior modeling assumptions. Our work will concentrate on a set of trajectories that replace the path space of the stochastic process. A thorough investigation will be pursued of several fundamental mathematical constructions that are available in this setting without any prior probabilistic assumptions.A trajectorial version of the fundamental notion of financial arbitrage offers the possibility to define a general notion of trajectorial martingale. The latter concept is the analogue of martingale processes and as such is poised to play a central role in our approach. Among many developments, we will construct a pathwise version of conditional expectations and will study the possibility to develop a trajectorial analogue of the different variants of pathwise stochastic integrals.A number of fundamental analytical developments are possible in the proposed framework. In particular, there is a natural integration operator defined by superhedging, a financial based approximation that provides coverage under each eventuality (trajectory wise) and which is not associated to a classical (Kolmogorov-type) probability measure.Our approach pays attention to individual trajectories and, as such, could also be labelled worst case. The latter concept gains relevance and specificity in each particular application where assuming an apriori probability distribution is unwarranted. Our proposal does not make any assumptions on probability distributions (i.e. measure) but explores basic results that can be obtained prior to introducing a measure. This allows to gain a conceptual understanding of the financial meaning of new and established mathematical results that are obtained in our framework as they are interpreted without the language of probabilities. We will explore the financial implications of our new conceptual approach and will propose several market model constructions.
金融市场是现代社会的重要组成部分;它们提供所需的资本,使无数的经济活动成为可能。令人遗憾的是,金融投机的消极一面以及廉价和无限信贷的可获得性产生了不良的副作用(例如市场崩溃、无法控制的债务等)。 简而言之,确实需要更好地了解金融市场。金融数学中的随机建模目前正被推广到更高层次的不确定性。 这一举措反映了模型目前无法纳入影响市场状况的所有变量以及可靠的联合概率分布。沿着这条现代研究路线,我们提出了一种方法,大大削弱了基本的随机建模假设。这种方法的结论更稳健,因为它们较少依赖于先前的建模假设。 我们的工作将集中在一组轨迹,取代随机过程的路径空间。 本文将深入研究在没有任何先验概率假设的情况下,金融套利的几个基本数学构造,并给出了金融套利基本概念的一个新版本,为定义一个广义的向量鞅提供了可能性。后一个概念是类似的鞅过程,因此是准备在我们的方法中发挥核心作用。在众多的发展中,我们将构建一个路径版本的条件期望,并将研究发展的可能性,以开发一个不同的变量的路径随机积分的阶乘模拟。一些基本的分析发展是可能的,在所提出的框架。特别是,有一个自然的整合运营商定义的超对冲,金融为基础的近似,提供覆盖下的每个可能性(轨迹明智的),这是不相关的经典(柯尔莫哥洛夫型)的概率measure.Our方法注意到个人的轨迹,因此,也可以被标记为最坏的情况。后一个概念在每个特定应用中获得相关性和特异性,其中假设先验概率分布是不必要的。我们的建议不对概率分布(即测度)做任何假设,而是探索在引入测度之前可以获得的基本结果。这使得我们能够从概念上理解在我们的框架中获得的新的和已建立的数学结果的金融含义,因为它们是在没有概率语言的情况下解释的。我们将探讨我们的新概念方法的财务影响,并将提出几个市场模型的建设。

项目成果

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Ferrando, Sebastian其他文献

Robust portfolio choice with derivative trading under stochastic volatility
  • DOI:
    10.1016/j.jbankfin.2015.08.033
  • 发表时间:
    2015-12-01
  • 期刊:
  • 影响因子:
    3.7
  • 作者:
    Escobar, Marcos;Ferrando, Sebastian;Rubtsov, Alexey
  • 通讯作者:
    Rubtsov, Alexey
Optimal investment under multi-factor stochastic volatility
  • DOI:
    10.1080/14697688.2016.1202440
  • 发表时间:
    2017-02-01
  • 期刊:
  • 影响因子:
    1.3
  • 作者:
    Escobar, Marcos;Ferrando, Sebastian;Rubtsov, Alexey
  • 通讯作者:
    Rubtsov, Alexey

Ferrando, Sebastian的其他文献

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{{ truncateString('Ferrando, Sebastian', 18)}}的其他基金

Trajectorial Martingales and Worst Case Approach to Market Models
轨迹鞅和市场模型的最坏情况方法
  • 批准号:
    RGPIN-2018-03867
  • 财政年份:
    2021
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
Trajectorial Martingales and Worst Case Approach to Market Models
轨迹鞅和市场模型的最坏情况方法
  • 批准号:
    RGPIN-2018-03867
  • 财政年份:
    2020
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
Trajectorial Martingales and Worst Case Approach to Market Models
轨迹鞅和市场模型的最坏情况方法
  • 批准号:
    RGPIN-2018-03867
  • 财政年份:
    2019
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
Trajectorial Martingales and Worst Case Approach to Market Models
轨迹鞅和市场模型的最坏情况方法
  • 批准号:
    RGPIN-2018-03867
  • 财政年份:
    2018
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."
“非概率金融数学。过程、小波和应用的离散化。”
  • 批准号:
    194624-2012
  • 财政年份:
    2017
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."
“非概率金融数学。过程、小波和应用的离散化。”
  • 批准号:
    194624-2012
  • 财政年份:
    2015
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."
“非概率金融数学。过程、小波和应用的离散化。”
  • 批准号:
    194624-2012
  • 财政年份:
    2014
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."
“非概率金融数学。过程、小波和应用的离散化。”
  • 批准号:
    194624-2012
  • 财政年份:
    2013
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."
“非概率金融数学。过程、小波和应用的离散化。”
  • 批准号:
    194624-2012
  • 财政年份:
    2012
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual
Adaptive martingale expansions applications to mathematical finance signal processing stochastic processes
自适应鞅将应用扩展到数学金融信号处理随机过程
  • 批准号:
    194624-2005
  • 财政年份:
    2009
  • 资助金额:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual

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稳态鞅和其他非高斯过程的推理方法
  • 批准号:
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  • 资助金额:
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轨迹鞅和市场模型的最坏情况方法
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  • 批准号:
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轨迹鞅和市场模型的最坏情况方法
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  • 资助金额:
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轨迹鞅和市场模型的最坏情况方法
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    RGPIN-2018-03867
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