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CAREER: An Approach to Pricing, Hedging, Stability, and Asymptotic Analysis in Financial Markets

职业：金融市场的定价、对冲、稳定性和渐近分析方法

基本信息

批准号：
1848339
负责人：
Oleksii Mostovyi
金额：
$ 42万
依托单位：
University of Connecticut
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1848339&HistoricalAwards=false
关键词：
CAREER Approach Pricing Hedging Stability

项目摘要

As financial markets have not only grown but have also become very complex, understanding both their qualitative and quantitative aspects are among highly active areas of research in mathematics. This award provides methods for pricing, hedging, stability and asymptotic analysis in financial markets. These projects will further our understanding of so-called incomplete markets (i.e., the markets which have a limited capability to offset risks) and the sensitivity of such markets to different types of perturbations and trading restrictions. The topics will lead to new developments in stochastic control, convex and stochastic analysis, to novel interdisciplinary research, and results applicable in the financial industry. Graduate students and post doctoral researchers are included in the work of the project.The first research topic is stability and asymptotic analysis of financial markets with respect to perturbations. Mathematically this topic leads to investigations of the responses of the underlying stochastic control problems to distortions of the input data. An appropriate form of parametrization for the perturbations and the corresponding value functions will allow for analysis involving only partial convexity (in one variable) of the underlying value function. Both dynamic and static formulations of the underlying stochastic control problem will be considered. The second topic is the pricing and hedging of financial instruments when additional trading constraints are imposed. This topic is connected to an investigation of the optimal investment problem with labor income, where extra trading constraints make the problem hard to analyze, and special forms of parametrization of the labor income and the value function are needed. The mathematical work relies on classical and modern results in stochastic analysis, stochastic control, finite and infinite-dimensional convex analysis, and new results to be established by the Principal Investigator.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着金融市场的发展，而且已经变得非常复杂，理解它们的定性和定量方面是数学研究中非常活跃的领域之一。该奖项提供金融市场定价，对冲，稳定性和渐近分析的方法。这些项目将进一步加深我们对所谓的不完全市场（即，抵消风险的能力有限的市场）以及这些市场对不同类型的扰动和交易限制的敏感性。这些主题将导致随机控制，凸和随机分析的新发展，新的跨学科研究，以及适用于金融行业的结果。本项目的研究对象包括研究生和博士后研究人员。第一个研究课题是关于扰动的金融市场的稳定性和渐近分析。在数学上，这一主题导致调查的基本随机控制问题的输入数据的扭曲的反应。适当形式的参数化的扰动和相应的价值函数将允许分析只涉及部分凸性（在一个变量）的基础价值函数。将考虑潜在的随机控制问题的动态和静态配方。第二个主题是当施加额外的交易限制时金融工具的定价和对冲。本课题研究的是有劳动收入的最优投资问题，由于存在额外的交易约束，使得问题难以分析，需要对劳动收入和价值函数进行特殊形式的参数化。数学工作依赖于随机分析、随机控制、有限维和无限维凸分析的经典和现代结果，以及首席研究员将要建立的新结果。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Stability and asymptotic analysis of theFöllmer–Schweizer decomposition on a finite probability space

有限概率空间上Föllmer-Schweizer分解的稳定性和渐近分析

DOI：
10.2140/involve.2020.13.607
发表时间：
2020
期刊：
a Journal of Mathematics
影响因子：
0
作者：
Boese, Sarah;Cui, Tracy;Johnston, Samuel;Molino, Gianmarco;Mostovyi, Oleksii
通讯作者：
Mostovyi, Oleksii

Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model

最优投资相对于半鞅模型扰动的二次展开