因應全球化影響，任何的財務金融市場都必須要考慮外來潛在的一些變因，並且，有時此一類型影響會有時間延遲的效應。因此，對於投資標的，我們提出延遲因子模型，更精確的說，我們假設投資標的動態過程的係數，是由另一隨機過程所構成，並且包含了時間延遲的特徵。因為時間延遲導致了此一過程為非馬氏鏈，造成應用傳統偏微分方程的困難，因此，我們採用機率的方法來處理此一問題，並且，提出三個特殊可解的例子來進行探討。此外，我們討論了承保方最佳化投資的問題。最後，根據高頻交易的特徵，我們應用隨機微分方程以及對數效用函數來尋找最佳化的投資策略，此外，我們在效用函數中考慮相對表現，亦即，投資人不只考想極大化自己的資產，更想進一步的極大化與平均資產的差距。 ;We propose a optimal portfolio problem where the underlying is driven by the factor model with delay feature in order to describe the interaction with time delay among different financial markets. The delay phenomenon can be recognized as the integral type and the pointwise type. Due to the delay leading to the non-Markovian structure, we obtain the optimal strategy through the coupled forward and backward stochastic differential equations (FBSDEs). The existence and uniqueness of the coupled FBSDEs are also studied. We analyze three particular cases where the corresponding FBSDEs can be solved explicitly. In addition, we consider the problem of optimal investment by an insurer where the claim size is driven by Brownian motion. The optimal strategy is obtained using the coupled FBSDEs. Finally, we analyze the model of high frequency trading in order to obtain the optimal ask quote based on the feature observed in financial markets under relative performance. The Nash equilibria are solved using the coupled Hamilton Jacobi Bellman (HJB) equations.
