应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2013年
5期
531-546
,共16页
最低身故利益保证%变额年金%体制转换模型%Esscher变换%快速傅里叶变换
最低身故利益保證%變額年金%體製轉換模型%Esscher變換%快速傅裏葉變換
최저신고이익보증%변액년금%체제전환모형%Esscher변환%쾌속부리협변환
Guaranteed minimum death benefit%variable annuity%regime-switching%Ess-cher transform%fast Fourier transform
本文研究具备最低身故利益保证的变额年金的定价问题。该模型中，假设无风险利率，投资基金的波动率是被连续时间有限状态马尔科夫链所调制的。运用体制转换Esscher变换方法得到唯一的等价鞅测度。在风险中性测度下，通过逆傅里叶变换得到最低身故利益保证的变额年金中嵌入期权的定价公式，然后通过快速傅里叶变换进行求解，并对数值例子进行了分析比较。
本文研究具備最低身故利益保證的變額年金的定價問題。該模型中，假設無風險利率，投資基金的波動率是被連續時間有限狀態馬爾科伕鏈所調製的。運用體製轉換Esscher變換方法得到唯一的等價鞅測度。在風險中性測度下，通過逆傅裏葉變換得到最低身故利益保證的變額年金中嵌入期權的定價公式，然後通過快速傅裏葉變換進行求解，併對數值例子進行瞭分析比較。
본문연구구비최저신고이익보증적변액년금적정개문제。해모형중，가설무풍험리솔，투자기금적파동솔시피련속시간유한상태마이과부련소조제적。운용체제전환Esscher변환방법득도유일적등개앙측도。재풍험중성측도하，통과역부리협변환득도최저신고이익보증적변액년금중감입기권적정개공식，연후통과쾌속부리협변환진행구해，병대수치례자진행료분석비교。
This paper considers the valuation of guaranteed minimum death benefit in variable annuities under a regime-switching model. More specifically, the risk-free interest rate, the appreciation rate and the volatility of the reference investment fund are modulated by a continuous-time, finite-state, observable Markov chain. A regime-switching Esscher transform is adopted to select an equiva-lent martingale measure in the incomplete financial market. Inverse Fourier transform is used to derive an analytical pricing formula for the embedded option in variable annuity with guaranteed minimum death benefit. To calculate the fair guarantee charge, fast Fourier transform approach is applied. Numerical examples are provided to illustrate the practical implementation and the relationship between the fair guarantee charges and other parameters.
