Actuarial Mathematics

9x+k A₁ actuarial present value Age Interval annual premium annuity approximation assume assumption b₁ calculate Chapter claim amount COLLECTIVE RISK MODELS commutation functions compound Poisson distribution death benefit decision maker decrement table deferred defined denoted distribution of deaths ECONOMICS OF INSURANCE effective annual rate equation equivalence principle Example expected expression force of interest force of mortality formulas fully continuous fully discrete fund future lifetime given Illustrative Life Table income INDIVIDUAL RISK MODELS insurance payable integral interpretation Jensen's inequality n-year term insurance notation obtain payment technique period policy issue PREMIUM RESERVES present-value random variable probability pure endowment reinsurance Section Show single premium Solution SURVIVAL DISTRIBUTIONS survival function survivorship group Theorem theory uniform distribution unit amount utility function vk+1 whole life insurance X₁