1 If T, and K, are random variables measuring the complete and curtate future lifetimes, respectively,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1 If T, and K, are random variables measuring the complete and curtate future lifetimes, respectively, of a life aged x, write down an expression for each of the following symbols as the expectation of a random variable: (i) (ii) Ax (0) (ii) xn 2 The benefit payable under a special assurance policy has present value random variable: W=max(K, +1,n) xn where K is the curtate future lifetime of a person currently aged exactly x. (i) Describe the benefit paid under this policy. Express E[W] in terms of standard actuarial notation. Express var[W] in terms of standard actuarial notation. 3 Calculate the expectation and standard deviation of the present value of the benefits from each of the following contracts issued to a life aged exactly 40, assuming that the annual effective interest rate is 4% and AM92 Ultimate mortality applies: a 20-year pure endowment, with a benefit of £10,000 a deferred whole life assurance with a deferred period of 20 years, under which the death benefit of £20,000 is paid at the end of the year of death, as long as this occurs after the deferred period has elapsed. (i) 4 Using an interest rate of 6% pa effective and AM92 Ultimate mortality, calculate: A¹ 50:15 (ii) A50:15 5 If /40=1,000 and /40+t=140-5t for t=1,2,...,10, calculate the value of A40:10] at 6% pa interest. 1 If T, and K, are random variables measuring the complete and curtate future lifetimes, respectively, of a life aged x, write down an expression for each of the following symbols as the expectation of a random variable: (i) (ii) Ax (0) (ii) xn 2 The benefit payable under a special assurance policy has present value random variable: W=max(K, +1,n) xn where K is the curtate future lifetime of a person currently aged exactly x. (i) Describe the benefit paid under this policy. Express E[W] in terms of standard actuarial notation. Express var[W] in terms of standard actuarial notation. 3 Calculate the expectation and standard deviation of the present value of the benefits from each of the following contracts issued to a life aged exactly 40, assuming that the annual effective interest rate is 4% and AM92 Ultimate mortality applies: a 20-year pure endowment, with a benefit of £10,000 a deferred whole life assurance with a deferred period of 20 years, under which the death benefit of £20,000 is paid at the end of the year of death, as long as this occurs after the deferred period has elapsed. (i) 4 Using an interest rate of 6% pa effective and AM92 Ultimate mortality, calculate: A¹ 50:15 (ii) A50:15 5 If /40=1,000 and /40+t=140-5t for t=1,2,...,10, calculate the value of A40:10] at 6% pa interest.
Expert Answer:
Answer rating: 100% (QA)
1 The symbols Ax and xl can be expressed as the expectation of a random variable as follows Ax EeTx xl EKx where Tx is the complete future lifetime random variable Kx is the curtate future lifetime ra... View the full answer
Related Book For
Principles of Communications Systems, Modulation and Noise
ISBN: 978-8126556793
7th edition
Authors: Rodger E. Ziemer, William H. Tranter
Posted Date:
Students also viewed these finance questions
-
This problem combines equilibrium analysis with some of the things you learned in the chapter on intertemporal choice. It concerns the economics of saving and the life cycle on an imaginary planet...
-
Average profit of a firm is Rs. 48.000. The rate of capitalization is 12%. Assets and liabilities of the firm are Rs. 4.00,000 and Rs. 1.70,000 respectively. Calculate goodwill.
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Draw a UML Sequence Diagram for the process involved in paying a vendor for an item in cash. The process to follow is below. [15 points] a) Go to the bank b) Request your account balance c) The bank...
-
Show that the time-dependent wave function given by Eq. (40.15) is a solution to the one-dimensional Schrodinger equation, Eq. (40.1).
-
Under what circumstances might a court deny a motion to extend time?
-
Discuss the ways in which a federated system can be formed. What are the key roles of the national board and the chapter boards? How do the national staff and the chapter staff best relate to this...
-
Gleason and Company is planning to invest $5 million in a new, stand-alone project. Before depreciation, it expects this project to yield a positive cash flow of $1.4 million each year for five...
-
The figure shows side-by-side box plots of the miles per gallon by vehicle origin. Miles per Gallon by Vehicle Origin 45 10 35 30 Miles per Gallon (MPG) 25 20 15 10 USA France Japan Germany Sweden...
-
Pin Cushion Company produces two models of sewing basket. Information about Pin Cushions products is given below: Pin Cushions fixed costs total $35,200. Required: 1. Determine Pin Cushions...
-
Which of the following is true regarding posting transactions into T-accounts in the ledger? Credits are posted on the left; debits are posted on the right. Debits are posted on the left; credits are...
-
Wildhorse Company purchased a machine at a price of $109,900 by signing a note payable, which requires a single payment of $142,324 in 3 years. Click here to view factor tables. Assuming annual...
-
29. A 50.0-kg projectile is fired at an angle of 30.0 above the horizontal with an initial speed of 1.20 x 102 m/s from the top of a cliff 142 m above level ground, where the ground is taken to be y...
-
What is your topic? Who is your target audience? Share examples of logos, pathos, and ethos you will include in the speech. What other persuasive techniques and/or appeals will you use? How will you...
-
Skater 1 (78 kg) and skater 2 (56 kg) are moving together going east. Skater 2 pushes skater 1 with a force of 64 N [W]. a) Determine the acceleration of each skater. b) What will happen to the...
-
Tamarisk Corporation donates equipment and a truck to the community Home Assistance Centre. The equipment had a cost of $110,000, accumulated depreciation to the contribution date of $51,000, and a...
-
This week's chapters speak about debt and lenders. What type of debt are you seeking to finance the purchase of FO and what type of bank or other financial institution is the most likely lender?...
-
During the year land was revalued and the surplus reported as Revaluation surplus; and an asset costing 80,000, written down to 38,000, was sold for 40,000. Identify the cost of any non-current...
-
Given these signals: Assume that they are used in a binary digital data transmission system in the following combinations. Express B and C in terms of A so that their energies are the same. Sketch...
-
Show that for M-ary QAM where E s is the symbol energy averaged over the constellation of M signals, which is (10.58). The summation formulas will prove useful. , a 2 (M 1) (+1) (+1)(2m + 1) ...
-
An NFSK receiver must be designed with additional bandwidth for the input filters to accommodate frequency uncertainty of the received signal (due to Doppler shift, for example). (a) Justify that the...
-
What circumstances might influence the growth or shrinkage of the nonprofit sector?
-
Discuss what a productive collaboration between a nonprofit, a for - profit, and the public sector might look like.
-
If you wanted to establish a homeless shelter in your community, what are the decisions and choices you would have to make along the way?
Study smarter with the SolutionInn App