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ACTSC232-Ch6 - Chapter 6 Premium calculations Chapter 6...

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Chapter 6 Premium calculations Chapter 6 Premium calculations ACTSC 232 Introduction to Actuarial Mathematics Tianxiang Shi Department of Statistics and Actuarial Science University of Waterloo Winter 2012 Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Outline 1 Introduction 2 Percentile principle 3 Equivalence principle Net premium Gross premium 4 Profit and extra risks Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Introduction Premiums Premium : the amount of money paid by the buyer (policyholder) to the insurer. often to be a series of contingent level payments paid at the beginning of each period in traditional life insurances Some insurances (e.g., Universal Life) offer great flexibility of the timing and amounts of the premiums single premium : a lump sum paid at the inception of an insurance contract Net premium : only cover the insurance benefit. also referred to, risk premium or benefit premium . Gross premium : not only cover insurance benefit, but also cover expenses and profit , etc. Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Introduction Loss-at-issue random variable Net loss-at-issue r.v. ( net future loss ): L n 0 = PV of benefit outgo - PV of net premium income Gross loss-at-issue r.v. ( gross future loss ): L g 0 = PV of benefit outgo + PV of expenses - PV of gross premium income Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Introduction Example: Net loss-at-issue random variable Example An insurer issues a whole life insurance to [60], with sum insured $1,000,000 payable immediately on death. Premiums are payable annually in advance, ceasing at age 80 or on earlier death. The net annual premium is P. Write down the net future loss random variable, L n 0 , for this type of contract in terms of life random variables for [60]. Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Introduction Premium determination principles There are several ways to determine premiums for a particular benefit. Equivalence principle : Net premium: EPV of benefit = EPV of premiums most common principle in traditional life insurance. we assume equivalence principle throughout this class unless otherwise specified . Gross premium: EPV of benefit + EPV of expenses = EPV of gross premiums under equivalence principle Net premium: set E [ L n 0 ] = 0 Gross premium: set E [ L g 0 ] = 0 Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Introduction Premium determination principles Cont’d Percentile principle : sets the premium at a level such that the probability for the insurer to suffer a loss is no larger than a given level. applies to individual case, or portfolio case (in this case, the normal approximation is usually involved). under percentile principle, for a small α Net percentile premium: set Pr( L n 0 > 0) α Gross percentile premium: set Pr( L g 0 > 0) = α Tianxiang Shi([email protected])
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Chapter 6 Premium calculations Percentile principle Percentile principle: individual case For each individual policy, set the premium to be the minimal P such that Pr( L 0 > 0) α
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