Stochastic Methods in Finance

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。

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.