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Assume that interest rates are positive, that is, the investment discount function v(t) is decreasing with t.
(a) Show that a‾ (1t; v) is a concave function of t.
(b) Use Jensen's inequality to show that a‾ (1ex? ) ≥ a‾x
(c) Now assume constant interest. A 1-unit whole life policy on (x) has premiums payable continuously at the annual rate of P. Show that P E[ValT(x)(1T(x); v)] ≥ 1.
That is, the expected amount of premiums accumulated at death by a policyholder is greater than or equal to the benefit payment at that time.
(d) Explain the inequality in (c) by general reasoning.
(e) Show that the inequalities in (b) and (c) are equalities at 0 interest.
if 5 is subtracted from the numerator of a fraction the value of the resulting fraction is 13. however if 5 is added
For all (smooth) polar curves r = f(θ), 0 ≤ θ ≤ π/2, with f(0) = 1 and f(π/2) = 1, and f(θ) ≥ 1 for all 0 ≤ θ ≤ π/2, show that their arc-lengths are greater than or equal to π/2.
You have to perform a reliability analysis of the downtime data.
Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 12. (Round your answers to four decimal places.)
An ATM personal identification number (PIN) consists of 4 digits. How many PIN's are possible?
finding the exact value of cosalpha-betalet cos alpha 2425 where alpha has its terminal side in the first quadrant and
The Jacksons plan a 3-Week trip with a budget of $600 for renting a car. Car rental rates are $135/week plus $0.17/km. Write a formula to show the number of kilometers the Jacksons can travel.
If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Find the three qualitatively different regimes of growth from the given data - formulation to distinguish and describe three qualitatively different regimes of growth
How do you determine how many observations to average in a moving average model? How do you determine the weightings to use in a weighted moving average model?
suppose the following game. a player rolls two dice. if the outcome on both dice is the same doubles the player wins 5.
Solve the differential equation
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