{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Part-4-Notes-232-2010W

# Part-4-Notes-232-2010W - Summary of Lecture Notes ACTSC 232...

This preview shows pages 1–3. Sign up to view the full content.

Summary of Lecture Notes – ACTSC 232, Winter 2010 Part 4 – Benefit Premiums The loss random variable L for an insurance or annuity is defined as L = The PV of benefits - The PV of premiums. The expectation of the loss random variable is E [ L ] = The APV of benefits - The APV of premiums. Equivalence Principle (EP): Set premiums such that E [ L ] = 0 or The APV of benefits = The APV of premiums. Percentile Principle (PP): Set premiums such that Pr { L > 0 } = α . Note that we assume the equivalence principle throughout this courses unless otherwise stated. 4.1 Fully continuous benefit premiums – In an insurance, the benefits of the insurance form a continuous life insurance while the premiums of the insurance form a continuous life annuity. (a) A fully continuous whole life insurance of 1 on ( x ) with an annual premium rate of ¯ P : L = v T x - ¯ P ¯ a T x , ¯ P = ¯ A x ¯ a x = δ ¯ A x 1 - ¯ A x = 1 - δ ¯ a x ¯ a x , V ar [ L ] = 1 + ¯ P δ ! 2 V ar ( v T ) = 1 + ¯ P δ ! 2 h 2 ¯ A x - ( ¯ A x ) 2 i = 2 ¯ A x - ( ¯ A x ) 2 ( δ ¯ a x ) 2 . (b) A fully continuous h -Payment whole life insurance of 1 on ( x ) with an annual pre- mium rate of ¯ P : L = v T x - ¯ P ¯ a T x h , ¯ P = ¯ A x ¯ a x : h . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(c) A fully continuous n -year term insurance of 1 on ( x ) with an annual premium rate of ¯ P : L = v T x - ¯ P ¯ a T x , T x n 0 - ¯ P ¯ a n , T x > n ¯ P = ¯ A 1 x : n ¯ a x : n . (d) A fully continuous n -year endowment insurance of 1 on ( x ) with an annual premium rate of ¯ P : L = v T x n - ¯ P ¯ a T x n , ¯ P = ¯ A x : n ¯ a x : n = δ ¯ A x : n 1 - ¯ A x : n = 1 - δ ¯ a x : n ¯ a x : n , V ar [ L ] = 1 + ¯ P δ !
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

Part-4-Notes-232-2010W - Summary of Lecture Notes ACTSC 232...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online