{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

RelativeResourceManager5

# RelativeResourceManager5 - 05 t(ii μ = 0.01(iii δ =...

This preview shows pages 1–5. Sign up to view the full content.

MATH 471: Actuarial Theory I Homework #5: Fall 2009 Assigned September 23, due October 7 1. Suppose mortality follows l x = 110 - x for 0 x 110 and i = 0.08. (a) Calculate ¯ A 1 25: 30 . (0.1377) (b) Calculate var ( Z ), where Z is the present value random variable for a 30-year term insurance issued to (25) that pays 1 at the moment of death. (0.0567) 2. Assume μ x + t = μ and δ t = δ for t 0. Show that: ¯ A x = μ μ + δ . [Note: Memorize this result!!!] 3. Let Z be the present value random variable for a special continuous whole life insurance issued to (x), where for t 0: (i) b t = 1000 exp[0

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 05 t ] (ii) μ = 0.01 (iii) δ = 0.06 (a) Calculate the actuarial present value of this insurance. (500) (b) Calculate the variance of Z . (83,333.33) 4. Let Z be the present value random variable for a continuous 20-year term insurance of 1 on (40). Assume mortality follows de Moivre’s Law with limiting age 100, and δ = 0.05. Show that the cdf of Z , F Z ( z ), is such that: F Z ( z ) = 0 for z < = 2 3 for 0 ≤ z < e-1 = 1 + ln( z ) 3 for e-1 ≤ z < 1 = 1 for z ≥ 1...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

RelativeResourceManager5 - 05 t(ii μ = 0.01(iii δ =...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online