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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.
Also, the shop will lose $75 per day at a sales level of x=0. Find the profit from operating the shop at a sales level of x ties per day.
Using law of cosines for solving the problem.
Find all points with coordinates of the form (a, a) that are a distance 4 from P(-1, 3). (x, y)=( ) (smaller x-value)
Suppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than 31 received C's and those with scores above 595 received A's. What are the mean and standard deviation of the scores?
How do you find the x intercepts in standard form
write an equation for the number of cups you sellnbspas a function of the price you charge.suppose you have a lemonade
Determine the time it takes the ball to reach its maximum height:
The person is a constant 93 feet away from the balloon's starting point and the angle that the rope makes with the ground increases at a rate of 0.01 radians/minute. How fast is the balloon rising when the angle is 0.6 radians?
how many of each should she order to maximize her profit if she can spend 1200 on buying costs 800 on selling cost and 500 on delivery costs?
when 1500 units are being produced, the level of production is increasing at the rate of 20 units per week. what it the ttal cost at this time, and at what rate is the total cost changing at that moment?
A machine produces widgets at a defective rate of 6%. A sample of 6 widgets is taken, What is the probability that less than 2 of them are defective?
a rock falls from a tower that is 288 feet high. as it is falling its height is given by the function h(t)=288-16t2. how many seconds will it take the rock to hit the ground (h=0).
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