本論文以蒙地卡羅模擬演算法為核心，選擇高科技業與金融業等兩個應用場景，分探討該方法如何在動態隨機的經營環境下，協助企業進行商業決策的應用。
第一篇論文以Optimal Outsourcing Strategy: A Stochastic Optimization Approach 為題，主要探討議題與成果如后：
由於企業的產能在一定期間內是有限制的，因此，產品線的自行製造與委外代工是生產事業的重要決策議題之一。本研究使用一公司的歷史資料，進行參數估計，並以蒙地卡羅方法模擬情境，決定各期最適公司委外代工數量，以極大化公司期望獲利。並考慮三種不同特性的外包合作夥伴，一為外包商完全能配合公司要求，二為雙方期初決定未來以固定比例外包，三為雙方期初決定未來以固定數量外包，與兩種簡單策略，為全數外包策略與產能用盡策略，分析與比較這五種情境下公司的獲利。其結果顯示，採用多期最適數量的隨機規劃模型，最適化後的策略能為公司節省500萬元以上的成本，最高可省去1500萬元，並提高約400萬元以上的淨利。本研究進一步分析三種特性的外包合作夥伴之間的優劣，以第一種特性的外包商獲利最高，當限制越多，會降低淨利。有別於傳統的文獻採用靜態或比較靜態分析決定最適生產，本文提出一個可以決定多期的自行製造或委外代工的最適數量的隨機規劃模型，它可以作為高科技產業在面對不確定需求狀態下，決定未來生產配置決策之參考方針，它也可以作為未來財務預測的依據，且能為公司省去成本，並提高獲利。

第二篇論文以 Fast Simulation of Operational Risk for Financial Institutions 為題，主要探討議題與成果如后：
近年來，作業風險的量化已經成為金融機構監理的一個重要議題。例如，保險監理 的 Solvency II 與銀行監理的巴塞爾協定都要求保險公司與銀行需要計提作業風險資本。在巴塞爾協定的進階測量方法 (Advanced Measurement Approaches) 下，金融機構有自由選擇使用的隨機模型。損失分配法 (Loss Distribution Approach) 是一個符合這個目的的標準隨機模型。在損失分配法下，事業單位與損失形態的組合組成一個矩陣; 而矩陣中的每一個元素有自己的損失分配。這些損失分配的相關性通常是透過 Copulas 來做連結。金融監理上對作業風險資本計提的需求, 通常是需要金融機構計算一年內，在99.9%的信賴度下，作業風險可能帶來的最大損失。在這樣的高標準要求下，傳統的蒙地卡羅法無法提供一個準確的估計值。因此，本論文最大的貢獻在於設計一個有效率的蒙地卡羅演算法，達成快速且正確計算作業風險值並且滿足金融監理對金融機構對作業風險的量化要求。

This dissertation utilizes Monte Carlo methods to solve business problems in hi-tech and financial companies. There are two essays:
The first one is titled “Optimal Outsourcing Strategy: A Stochastic Optimization Approach”：
As the production capacity of a company over a certain period of time is limited, enterprises must carefully consider product line development or outsourcing options. Unlike traditional studies that use static or comparative static analyses to determine optimal production strategies, essay 1 proposes a stochastic optimization model that can be used to determine optimum quantities of multi-period production/outsourcing plans. Based on the proposed approach and utilizing the real demand and production capacity data of a high-tech production company in Taiwan, we can quantify the expected financial benefit of an optimal outsourcing strategy. In addition, we consider 3 types of outsourcing partners. The type of outsourcing partners is based on their flexibility to accept outsourcing requests. Therefore, the proposed approach can be applied to a broad range of possible outsourcing partners and can quantify the benefits of flexibility in outsourcing requests.
The second essay is titled “Fast Simulation of Operational Risk for Financial Institutions”：
Quantification of operational risk has led to significant concern regarding regulation in the financial industry. Basel Accord II and III for banks and Solvency II for insurers require insurance companies and banks to allocate capital for operation risk. Because the risk measure used for Basel regulatory capital purposes reflects a confidence level of 99.9% during one year and the loss distribution of operational risk has high skewness and kurtosis, it is almost infeasible to get an accurate estimate of such a risk measure if a crude Monte Carlo approach is used. Therefore, we develop a novel importance sampling method for estimating such a risk measure. Numerical results demonstrate that the proposed method is very efficient and robust. The main contribution of this method is to provide a feasible and flexible numerical approach that delivers highly accurate estimates of operational risk with a high confidence level and meets the high international regulatory standard for quantification of operational risk.

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