The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed bene ts. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner. In an attempt to nd low-cost and efficient alternatives, we explore the techniques of comonotonic bounds to produce closed-form approximation of the risk measures for variable annuity guaranteed bene ts. The techniques are further developed in this paper to address in a systematic way risk measures for death bene ts with the consideration of dynamic policyholder behavior.
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