保本型變額壽險之評價分析

• Main Author: 郭怡馨
• Language: 中文
• Published: 國立政治大學
• Subjects: 保本型變額壽險; 平賭理論
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002001714%22.

本研究是以保本型變額壽險的評價分析為節疇，保本型變額壽險屬於「利率敏感型」的壽險保單，保險給付與契約所明定的投資組合及最低保證利率相關，與傳統保險在評價過程上存在明顯的差異。本文分別以躉繳生存保險、躉繳定期保險、定期繳生存保險及分期繳定期保險四種基本類型的保險為研究的對象，應用選擇權計價的平賭理論及財務經濟的套利定價模型，同時配合人壽保險死亡風險分攤的特性，建構附有最低保證給付變額壽險的定價模式，進而計算保本型變額壽險的保費。 針對分期繳生存險及定期險的給付方式，假設保戶所持有的指定投資資產單位數為已知常數，以避免計算保費時無數值解的情形。由保費的計算，進一步利用未來法評估保險人所應提存的市價準備金，並利用Thiele偏微分方程式探討精算及財務假設隨時間改變時對於市價準備金所產生影響。 最終以臺股指數（TAIEX）為假定的投資組合對保本型變額壽險進行數值分析，探討金融環境及保險人保證利率變動時，對於保本型變額壽險保費的敏感程度。因保本型變額壽險保費與指定投資組合及保證利率的連動性，得到下列顯著的結果：於定期險中，死亡風險的影響遠大於選擇權的成本，因此保費的敏感程度較生存險為小；於分期繳生存險，保費並非隨無風險利率增加而遞減，因此最低的保費存在特定的無風險利率值；而於分期繳定期險，保費隨無風險利率的增加而增加。 === This study explores the practical applications on evaluation of net premiums for the variable life insurance policies with endogenous minimum guarantees. Four basic insurance policies are separately studied: the single and periodic premium(s) for guaranteed unit-linked pure endowment and term life insurance. Arbitrage pricing model and the theory of martingales provide a powerful technique for the analysis of equilibrium prices. Risk sharing methodology is employed to derive the premium under a specific reference portfolio for different variable life insurance policies, and extend them to the case where the minimum guarantees are endogenous. In pricing the periodic premiums for pure endowment and term life insurance, the number of shares of the reference portfolio is assumed to be known. Hence the premium can be solved by numerical methods. The partial differential equations of the reserve for the variable life insurance with endogenous minimum guarantees are also explored. A connection between the celebrated Black and Scholes partial differential equation encountered in financial economics and the familiar Thiele’s differential equation from the theory of the life insurance are found. Finally, the variable life insurance policies linked to the Taiwan Average Index of Stock Exchange (TAIEX) are studied for numerical illustrations. Sensitivity analyses of the premiums under plausible scenarios are explored. Some significant results are reported.