シンプルな生命保険

R による生命保険商品の評価

Roel Verbelen, Ph.D.

Statistician, Finity Consulting

生命保険

$\quad \,$ EPV は

$$ {}_{k|1}A_{x} = 1 \cdot \ v(k+1) \cdot \ {}_kp_x \cdot \ q_{x+k} = 1 \cdot \ v(k+1) \cdot \ {}_{k|}q_{x} \, . $$

定数 $i = 3\%$ のとき ${}_{5|1}A_{65} = 1 \cdot \ v(6) \cdot \ {}_{5|}q_{65} = 1 \cdot \ v(6) \cdot \ {}_5p_{65} \cdot \ q_{70} $ を計算します。

# Mortality rates and one-year survival probabilities
qx <- life_table$qx
px <- 1 - qx

# 5-year deferred mortality probability of (65) 
kpx <- prod(px[(65 + 1):(69 + 1)])
kqx <- kpx * qx[70 + 1]
kqx

0.02086664

# Discount factor
discount_factor <- (1 + 0.03) ^ - 6
discount_factor

0.8374843

# EPV of the simple life insurance
1 * discount_factor * kqx

0.01747548

R による生命保険商品の評価