Stochastic optimal control in mathematical finance

数学金融中的随机最优控制

基本信息

  • 批准号:
    RGPIN-2018-03978
  • 负责人:
  • 金额:
    $ 1.31万
  • 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

Over the last several decades the role of mathematical methods in financial decision making has steadily increased, to the point that a distinct discipline of research and practice has developed under the rubric of "mathematical finance" or "financial engineering", the general goal of which is to establish a scientific approach for the efficient allocation of capital in an economy. In this approach one first builds an idealized mathematical model (or description) of the central aspects of the financial market within which the allocation of capital takes place. Then, with reference to this mathematical model, one can formulate in precise terms the problems with which financial decision making is concerned. Of particular importance is the problem of allocating capital in order to minimize risk or maximize returns on the capital invested (this is known as portfolio optimization).The focus of our research program will be on portfolio optimization subject to constraints on capital investment. Constraints can take the form of direct restrictions on investment (usually known as "portfolio constraints"), which are often imposed by regulatory agencies (for example a prohibition on short selling certain designated securities), but may also take the form of indirect restrictions on investment, in particular the stipulation of a "floor-level" below which the wealth of an investor must never fall regardless of how the market evolves. This latter constraint enforces a hard limit on possible losses in the course of financial trading (this is known as "portfolio insurance"). Constraints on capital investment are a natural part of financial decision making and are therefore of clear importance, and indeed portfolio optimization subject to only direct restrictions on investment (i.e. portfolio constraints alone) has received significant attention in the established literature. Considerably less attention has been devoted to portfolio optimization when one has the combination of both direct restrictions on investment (i.e. portfolio constraints) together with indirect restrictions on investment in the form of a stipulated lower bound on wealth (i.e. portfolio insurance), possibly because this combination of constraints does exhibit some clear and definite challenges which are not encountered when one deals with only direct restrictions in investment (i.e. portfolio constraints). The goal of the research in this proposal is to address portfolio optimization with such combined constraints, building on an approach and some partial results which we have already established for this problem. We expect that this will contribute to the advancement of knowledge in financial engineering. In particular, constraints which define a lower bound on wealth serve to limit losses in the course of portfolio optimization, thus helping to stabilize financial trades, with clear benefits to the Canadian economy.
在过去的几十年里,数学方法在金融决策中的作用稳步增加,以至于在“数学金融”或“金融工程”的范畴下发展了一门独特的研究和实践学科,其总体目标是建立一种科学的方法,在一个经济体中有效地配置资本。在这种方法中,人们首先建立一个关于金融市场中心方面的理想化数学模型(或描述),资本配置发生在这些方面中。然后,参照这个数学模型,可以精确地表述与财务决策有关的问题。特别重要的是资本分配问题,以最小化风险或最大化投资资本的回报(这称为投资组合优化)。我们的研究计划的重点将是受资本投资约束的投资组合优化。限制可以采取对投资的直接限制(通常称为“投资组合限制”)的形式,这通常是由监管机构施加的(例如,禁止卖空某些指定证券),但也可以采取对投资的间接限制的形式,特别是规定一个“最低限度”,无论市场如何发展,投资者的财富不得低于这个“最低限度”。后一种限制对金融交易过程中可能的损失施加了硬性限制(这被称为“投资组合保险”)。对资本投资的约束是金融决策的自然组成部分,因此具有明显的重要性,事实上,只受直接投资限制(即仅受投资组合约束)的投资组合优化在已有的文献中得到了相当大的关注。当一个人将对投资的直接限制(即投资组合限制)和以规定的财富下限(即投资组合保险)形式对投资的间接限制结合在一起时,对投资组合优化的关注要少得多,这可能是因为这种限制的组合确实显示出一些明确和明确的挑战,当一个人只处理投资的直接限制(即投资组合限制)时,这些挑战是不会遇到的。本提案中研究的目标是在我们已经为这个问题建立的一种方法和一些部分结果的基础上,解决具有这种组合约束的投资组合优化问题。我们预计,这将有助于提高金融工程方面的知识。特别是,界定财富下限的约束条件有助于限制投资组合优化过程中的损失,从而有助于稳定金融交易,对加拿大经济有明显的好处。

项目成果

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Heunis, Andrew其他文献

Heunis, Andrew的其他文献

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{{ truncateString('Heunis, Andrew', 18)}}的其他基金

Stochastic optimal control in mathematical finance
数学金融中的随机最优控制
  • 批准号:
    RGPIN-2018-03978
  • 财政年份:
    2021
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic optimal control in mathematical finance
数学金融中的随机最优控制
  • 批准号:
    RGPIN-2018-03978
  • 财政年份:
    2020
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic optimal control in mathematical finance
数学金融中的随机最优控制
  • 批准号:
    RGPIN-2018-03978
  • 财政年份:
    2019
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic optimal control in mathematical finance
数学金融中的随机最优控制
  • 批准号:
    RGPIN-2018-03978
  • 财政年份:
    2018
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic control, stochastic algorithms, and nonlinear filtering
随机控制、随机算法和非线性滤波
  • 批准号:
    6673-2010
  • 财政年份:
    2016
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic control, stochastic algorithms, and nonlinear filtering
随机控制、随机算法和非线性滤波
  • 批准号:
    6673-2010
  • 财政年份:
    2013
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic control, stochastic algorithms, and nonlinear filtering
随机控制、随机算法和非线性滤波
  • 批准号:
    6673-2010
  • 财政年份:
    2012
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic control, stochastic algorithms, and nonlinear filtering
随机控制、随机算法和非线性滤波
  • 批准号:
    6673-2010
  • 财政年份:
    2011
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Stochastic control, stochastic algorithms, and nonlinear filtering
随机控制、随机算法和非线性滤波
  • 批准号:
    6673-2010
  • 财政年份:
    2010
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Nonlinear filtering, stochastic control, stohastic algorithms
非线性滤波、随机控制、随机算法
  • 批准号:
    6673-2004
  • 财政年份:
    2008
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual

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