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.

拟议研究的目标是为财务应用开发数学模型和理论，并将结果应用于金融市场。大多数财务理论都有隐含的假设，即交易者可以按照立即交易的方式买卖或出售尽可能多的证券股。但是在实际市场中，这种假设不满足，因此“流动性风险”受到广泛关注。由于交易的时间和规模，流动性风险是市场上的额外风险。价格过程可能取决于交易者的活动，尤其是交易量。投资者的最佳交易策略和最佳清算问题需要从实践和数学方面进行研究。许多理论发展允许金融机构（例如银行）设计专门的衍生产品，找到“公平”的价格并将其出售给客户。障碍选项是一类广泛使用路径依赖的金融衍生品。链式选项被视为屏障选项，从某种意义上说，在基本资产价格越过主要障碍后，另一个障碍选项会变得活跃。这些链式式障碍选择在非处方股票和外汇衍生品市场中变得很流行，定价和对冲问题当然是重要的研究问题。对链式选项的研究起源于我自己（与D. Jun合着），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选择的范围，并了解此类产品的经济利益。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。该领域的数学研究非常重要，应该鼓励。