Stochastic Methods in Finance

金融中的随机方法

• 批准号: 293274-2013
• 负责人: Ku, Hyejin
• 金额: $ 0.8万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635985
• 关键词: Stochastic; Methods; Finance

The objectives of the proposed research are to develop the mathematical models and theory for financial applications and to apply the results to financial markets. Most finance theory has the implicit assumption that traders can buy or sell as many shares of securities as they wish by immediate transactions. But in actual markets, this assumption is not satisfied, and thus the subject "liquidity risk" has received wide attention. Liquidity risk is the additional risk in the market due to the timing and size of a trade. The price process may depend on the activities of traders, especially the trading volume. The optimal trading strategy for the investor and the optimal liquidation problems need to be investigated from the aspects of practice as well as mathematics. Many of the theoretical developments allow financial institutions (such as banks) to design specialized derivatives, find a "fair" price, and sell them to their clients. Barrier options are a widely used class of path-dependent financial derivatives. Chained option is viewed as barrier options which are chained together in a sense that another barrier option becomes active after underlying asset price crosses a primary barrier. These chained-type barrier options have become popular in the over-the-counter equity and foreign exchange derivatives market, and pricing and hedging problems are certainly important research questions. The research on chained option is originated by myself (co-authored with D. Jun), and it is a highly significant discovery. Our theoretical advances would help market participants enlarge the range of their choice and understand the economic benefits of such products. Efficient risk management is essential to the success of financial institutions such as investment banks and insurance companies. Mathematical research in this area is extremely important and should be encouraged.

拟议研究的目标是开发金融应用的数学模型和理论，并将结果应用于金融市场。大多数金融理论都有一个隐含的假设，即交易者可以通过即时交易买卖尽可能多的证券份额。但在实际市场中，这一假设并不成立，因此流动性风险这一课题受到了广泛的关注。流动性风险是由于交易的时间和规模而导致的市场额外风险。价格过程可能取决于交易者的活动，特别是交易量。投资者的最优交易策略和最优变现问题需要从数学和实践两个方面来研究。许多理论的发展允许金融机构（如银行）设计专门的衍生品，找到一个“公平”的价格，并出售给他们的客户。障碍期权是一种广泛使用的路径依赖型金融衍生工具。链式期权是指当标的资产价格越过一个主要障碍后，另一个障碍期权开始活跃的一种意义上的障碍期权。这些连锁型障碍期权在场外股票和外汇衍生品市场上非常流行，定价和套期保值问题无疑是重要的研究问题。对链式期权的研究是本人（与D.这是一个非常重要的发现。我们的理论进步将有助于市场参与者扩大他们的选择范围，并了解这些产品的经济效益。有效的风险管理对于投资银行和保险公司等金融机构的成功至关重要。这方面的数学研究极为重要，应予以鼓励。