Statistics is a branch of mathematics which is heavily employed in the area of Actuarial Mathematics. This thesis first reviews the importance of statistical distributions in the analysis of insurance problems and the applications of Statistics in the area of risk and insurance. The Normal, Log-normal, Pareto, Gamma, standard Beta, Frechet, Gumbel, Weibull, Poisson, binomial, and negative binomial distributions are looked at and the importance of these distributions in general insurance is also emphasized. A careful review of literature is to provide practitioners in the general insurance industry with statistical tools which are of immediate application in the industry. These tools include estimation methods and fit statistics popular in the insurance industry. Finally this thesis carries out the task of fitting statistical distributions to the flood loss data in the 50 States of the United States.

受2008年金融海嘯影響，人壽保險業因資本及信用市場之系統性風險而導致帳列資產價值大幅減損，進一步影響壽險公司清償能力，而主管機關為兼顧審慎監理與市場穩定原則，而採行資本監理寬容措施，卻使得資本不足之保險公司缺口擴大。另外，保險安定基金以保費為基礎徵收單一費率，加劇保險公司間交叉補貼之情形。因此，如何透過以責任準備金為基礎，計算公平合理之風險差別費率，以避免產生影響其他保險公司正常經營之系統性風險，抑或引發保險公司道德風險，為本文研究之主要議題。 本文與過去文獻主要之差異為：(1) 資產模型依資產配置方式，使用蒙地卡羅模擬詳盡現金流路徑，著重於描述壽險業之情境；(2) 股票型風險性資產加入跳躍過程 (Jump) 與隨機波動兩種情境，以表達壽險業資產端承受資本市場變動加劇之風險；(3) 考慮政府監理寬容措施，以描述主管機關對於壽險業監理態度。 依蒙地卡羅模擬法試算保險安定基金公平費率，研究結果發現：(1)監理寬容期限增加時，安定基金公平費率增加；(2)監理標準提高，安定基金公平費率有先降後升之效果；(3)保險公司財務槓桿比例增加時，安定基金公平費率上升。 / Due to the global financial crisis in 2008 that resulted in systematic risks in the equity and credit market, it creates significant deprecation in the life insurers’ balance sheet which affect insurers’ solvency. In order to retain prudent supervision and market stability, the authority has announced capital temporal relief plan that may make insolvency insurer worse. Recent occurrences of financial distress to some insurers have raised questions about whether the current guaranty system that charge a flat levy rate in premium-based is adequate to protect policyholders. A risk-weighted levy rate in reserve-based has been proposed to establish reasonable contribution method which can avoid high risk insurers’ moral hazard and protect the other insurers from further systematic risks. A brief summary of the advantages of this paper is listed below：(1) By Monte Carol simulation method, detailed cash flow of insurer’s asset allocation can be used to describe the risk preference of life insurer. (2) Our stock model incorporates jump diffusion and stochastic volatility in order to reflect that life insurers face increasing volatility in capital market. (3) Consider regulatory forbearance to represent government’s attitude to life insurers. We calculate fair guaranty premium through Monte Carol simulation method. We find that： (1) Fair premium increases as extending the period of regulatory forbearance. (2) As regulatory criterion raises fair premium decreases at first, but increases if regulatory criterion reaches certain level. (3) Increasing leverage ratio of the insurer results in increasing fair premium.