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.

由于金融市场不仅增长了，而且变得非常复杂，因此了解它们的定性和定量方面都是数学研究的高度活跃领域。该奖项提供了金融市场中定价，套期保值，稳定和渐近分析的方法。这些项目将进一步了解我们对所谓不完整市场的理解（即，抵消风险能力的市场有限）以及此类市场对不同类型的扰动和交易限制的敏感性。该主题将导致随机控制，凸和随机分析的新发展，以进行新的跨学科研究，并适用于金融行业。研究生和博士后研究人员被包括在项目的工作中。第一个研究主题是对金融市场的稳定性和渐近分析。从数学上讲，该主题导致对潜在随机控制问题对输入数据扭曲的响应进行了研究。用于扰动和相应值函数的参数化形式的适当形式将允许仅涉及基础值函数的部分凸度（一个变量）的分析。将考虑潜在随机控制问题的动态和静态公式。第二个主题是当施加其他交易限制时，金融工具的定价和对冲。该主题与对劳动收入的最佳投资问题的调查有关，劳动收入的额外交易限制使问题难以分析，并且需要对劳动收入的参数化和价值功能的特殊形式。数学工作取决于随机分析，随机控制，有限和无限二维凸分析的经典和现代结果，以及首席研究员将建立的新结果。该奖项反映了NSF的法定任务，并已通过评估该基金会的知识功能和广泛的影响来评估NSF的法定任务。

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