金融機構在決策過程中常面臨市場狀態無法完全觀察的不確定性，同時亦須考量與同業之間的相對績效競爭，因此如何在部分資訊下進行最適決策成為重要研究議題。本研究結合平均場賽局（Mean Field Game）與部分資訊的概念，建構一個銀行系統之隨機控制模型，探討銀行如何選擇其最適風險暴露程度。模型中假設市場報酬率無法直接觀察，銀行透過可觀察的市場訊號與濾波方法持續更新對隱藏市場狀態的信念，並將該信念納入決策過程。首先建立其對應的 Hamilton–Jacobi–Bellman 方程式，利用二次型價值函數擬設推導最適控制策略，並將問題化簡為 Riccati 偏微分方程組，進一步證明其解的存在性與驗證定理，以確認所得控制策略構成封閉迴路 Nash 均衡。最後透過數值模擬，比較基準模型、完全資訊模型與部分資訊模型之差異，分析係數函數、最適控制、橫截面離散程度、對數資本分布及警示事件分布。研究結果顯示，引入狀態相依係數會改變係數函數、增加終端對數資本分布的變異程度，並提高最嚴重警示事件發生的機率；而在本文參數設定下，部分資訊主要影響個別銀行之信念更新與對數資本演化，對整體系統結果的影響相對有限。;Financial institutions often make decisions under uncertainty regarding unobservable market conditions while simultaneously facing relative performance concerns. Consequently， studying optimal decision-making under partial information has become an important research topic. This study combines Mean Field Games with partial information to formulate a stochastic control model for a banking system and investigates how banks choose their optimal level of risk exposure. The model assumes that the market return is unobservable; banks update their beliefs about the hidden market state through observable market signals and filtering techniques， and incorporate these beliefs into their decision-making process. We derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation. By introducing a quadratic ansatz for the value function， the optimal control is characterized explicitly， and the problem is reduced to a system of Riccati-type partial differential equations. We further establish the existence of the PDE solution and prove a verification theorem， showing that the resulting feedback control constitutes a closed-loop Nash equilibrium. Finally， numerical experiments compare the baseline， full-information， and partial-information models. The coefficient function， optimal control， cross-sectional dispersion， log-capital distribution， and warning-event distribution are examined. The results show that state-dependent coefficients change the coefficient function， increase the variability of the log-capital distribution， and raise the probability of the most severe warning events. Under the parameter setting proposed in this study， partial information mainly influences individual banks′ belief updating and log-capital evolution， while having only a limited impact on the aggregate outcomes.
