| Abstract: |
The authors use the efficient hedging methodology for optimal pricing and
hedging of equitylinked life insurance contracts whose payoff depends on the
performance of several risky assets. In particular, they consider a policy
that pays the maximum of the values of <em>n</em> risky assets at some
maturity date <em>T</em>, provided that the policyholder survives to
<em>T</em>. Such contracts incorporate financial risk, which stems from the
uncertainty about future prices of the underlying financial assets, and
insurance risk, which arises from the policyholder's mortality. The authors
show how efficient hedging can be used to minimize expected losses from
imperfect hedging under a particular risk preference of the hedger. They also
prove a probabilistic result, which allows one to calculate analytic pricing
formulas for equity-linked payoffs with <em>n</em> risky assets. To illustrate
its use, explicit formulas are derived for optimal prices and expected hedging
losses for payoffs with two risky assets. Numerical examples highlighting the
implications of efficient hedging for the management of financial and
insurance risks of equity-linked life insurance policies are also provided. |