This paper considers an optimal life insurance for a householder subject to
mortality risk. The household receives a wage income continuously, which is
terminated by unexpected (premature) loss of earning power or (planned and
intended) retirement, whichever happens first. In order to hedge the risk of
losing income stream by householder's unpredictable event, the household enters
a life insurance contract by paying a premium to an insurance company. The
household may also invest their wealth into a financial market.