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principles of risk management

Questions and Answers of Principles Of Risk Management

Why are FIs among the most regulated sectors in the world? When is the net regulatory burden positive? LO.1
What is mortgage redlining? LO.1
If financial markets operated perfectly and costlessly, would there be a need for financial institutions? LO.1
What is negative externality? In what ways do the existence of negative externalities justify the extra regulatory attention received by financial institutions? LO.1
What is denomination intermediation? How do FIs assist in this process? LO.1
What are two of the most important payment services provided by financial institutions? To what extent do these services efficiently provide benefits to the economy? LO.1
What is this wealth transfer process? LO.1
Which intermediaries best fulfill the intergenerational wealth transfer function? LO.1
What is meant by credit allocation regulation? What social benefit is this type of regulation intended to provide? LO.1
How do depository institutions such as commercial banks assist in the implementation and transmission of monetary policy? LO.1
What are five areas of institution-specific FI specialness and which types of institutions are most likely to be the service providers? LO.1
What is maturity intermediation? What are some of the ways the risks of maturity intermediation are managed by financial intermediaries? LO.1
How can individual savers use financial institutions to reduce the transaction costs of investing in financial assets? LO.1
How can financial institutions invest in high-risk assets with funding provided by low-risk liabilities from savers? LO.1
How do financial institutions help individual savers diversify their portfolio risks? Which type of financial institution is best able to achieve this goal? LO.1
How do FIs alleviate the problem of liquidity risk faced by investors who wish to buy in the securities issued by corporations? LO.1
How do large FIs solve the problem of high information collection costs for lenders, borrowers, and financial markets? LO.1
What are agency costs? How do FIs solve the information and related agency costs when household savers invest directly in securities issued by corporations? LO.1
What are five general areas of FI specialness that are caused by providing various services to sectors of the economy? LO.1
Explain how financial institutions act as delegated monitors. What secondary benefits often accrue to the entire financial system because of this monitoring process? LO.1
In what sense are the financial claims of FIs considered secondary securities, while the financial claims of commercial corporations are considered primary securities? How does the transformation
Identify and explain the two functions FIs perform that would enable the smooth flow of funds from household savers to corporate users. LO.1
Identify and explain three economic disincentives that would dampen the flow of funds between household savers of funds and corporate users of funds in an economic world without financial
Explain how economic transactions between household savers of funds and corporate users of funds would occur in a world without financial institutions.LO.1
What are five risks common to financial institutions?LO.1
Derive each of the following formulae:AppendixLO1 (a) Px:n\ Ax:n\ ax:n (b) Px ===== d ax (c) Px:n] = ax:n x:n (d) Px = Ax x:1 = MxMx+n+Dx+n Na - Notn x+n -d Mx N - NH
A life insurance policy is issued at age 30. The initial death benefit is 10,000. At age 40 and each year thereafter, the death benefit increases by 5000 per year for ten years. No death benefit is
Repeat Question 52 if the death benefits do not stop after 20 years, but increase indefinitely by 5000 per year, and if the premiums are payable for as long as the purchaser survives.
Aloysius, aged 40, purchases a life policy. Before age 60, the death benefit is the sum of the net premiums paid. At age 60 and later, the death benefit is 20,000. Find the net annual premium,
Repeat Question 54 if the death benefit before age 60 is the sum of the net premiums paid plus interest.
Ellen, aged 60, purchases a life insurance policy paying 50,000 until age 65, 25,000 at age 65 and decreasing by 2500 per year thereafter until it reaches 5000, at which point it remains
A 10,000 term insurance policy for 20 years is issued at age 45.The net annual premium for the first year is X and for each year thereafter is 2X. Find X in each of the following cases:(a) M45 - 800,
Roy, aged 50, purchases a whole life policy of 10,000 with a series of annual payments contingent on survival. Find the amount of each payment in each of the following cases:(a) M5o= 150andiV50 =
(a) If the force of interest is increased, but the force of mortality stays the same, does A ^ increase or decrease? Explain your answer,(b) If the force of mortality is increased, but the force of
Douglas is hired by XYZ Publishing Company at age 50, and will retire when he turns 65. On his 62"^ birthday he becomes eligible for a death benefit paying 1000 for each year of service with XYZ.The
A whole life insurance policy is sold to the family of a newborn child. The policy pays 1000 if death occurs in the first year, 2000 in the second year, and so on up to 10,000 in the tenth year. The
Derive each of the following identities:(a) {IA\ = v{Id\ - {Ia\(b) {IA\ = d,- d{Id\AppendixLO1
Do Question 40 if the insurance policy begins with an initial benefit at 120,000, and then decreases by 6000 annually until it reaches zero. Assume the data given in Questions 40 and 41.
Repeat Question 40 if Tim's policy is to increase as stated up to and including age 70, and then remain constant at 120,000 per year thereafter. Use the data given in Questions 40 and 41.
A 100,000 whole life policy is issued at age 25. Premiums are payable at the beginning of each year for life, and death benefits are payable at the end of the year of death. The following are
Repeat Question 56 if an extra expense of 3 is required at the beginning of every year throughout the policy.
A whole life insurance policy is issued at age 30. The gross annual premium is 120 payable at the beginning of each year for life. Expense provisions include 50% of the first year's gross annual
Under "normal" circumstances, we would expect /F;^ > 0. Why?AppendixLO1
As with premiums, reserves where the payments are made continuously are denoted by placing a bar over the V, and reserves where the insurance is payable at the moment of death are denoted by
Assuming 6 = .07 and ^^ = .04 for all x, find each of the following:AppendixLO1 (a) P(Ax) (b) Px (c) P(Ax) (d) P(A5)
Show that.AppendixLO1 1Vx = 1 - (1-1Vx)(1-1Vx+1)(1-1Vx+1-1).
Show that.AppendixLO1 V = Axti (1+1+1Px) - 1 Pr Vx Ax+1
Find ,+|F, given A = .013, ,F^ = A3,q^+, = .004 and / = .03.AppendixLO1
Betty, aged 40, purchases a 100,000 whole life policy with a single premium of 36,000. At the same time, Betty also purchases a 100,000 whole life policy with a net annual premium of 2200 payable at
Repeat Question 65 if the death benefit, instead of having a face value of 50,000, is a 20-year interest-only annuity of 5000 per year with the first payment at the end of the year of death.
Benjamin, aged 35, purchases a 30-year term insurance policy with a face value of 50,000. Level premiums are payable at the beginning of each year for the next 20 years. Assume / = .03, A^35 = 7300,
Show that u.-x-\ ^x = ^ — Px, where u; is the terminal age of the population.AppendixLO1
Rosalita, aged 20, purchases a whole life policy paying 5000 the first year and increasing by 5000 per year thereafter. She pays annual premiums at the beginning of each year of Jf for the first 10
Morgan, aged 40, purchases a whole life policy paying 50,000 in case of death within the next 10 years and 100,000 thereafter.Assume M40 = 740, M50 = 580 and N^q = 59,000.(a) Find the net annual
Derive a formula in terms of commutation functions for the gross annual premium at age x, payable for n years, for a whole life insurance policy of 1, if the expenses consist of a flat amount of h
A life insurance policy issued at age 50 provides a death benefit of 10,000, less the sum of the gross annual premiums which would otherwise be paid after the date of death. Premiums are paid at the
A deferred life annuity, issued at age 35, will provide monthly payments of 1000 commencing at age 65. Annual premiums are payable at the beginning of each year for 20 years. During the deferred
Repeat Question 40 if Tim's policy is only to last for 20 years. In addition to the above data, assume M-jo = 60 and R-jo = 400.
Tim, aged 50, purchases a whole life policy. In the first year his benefit is 20,000, and benefits increase by 5000 per year thereafter. Find the net single premium given Dso = 500, Rso = 2300 and
Repeat Question 9 if the insurance is paid at the end of the year in which the first of the two men dies.
Repeat Question 9 if the policy is for 2-year endowment insurance.
Prove the identity ^;f = v^q^ -\-pxAx+]).
Give a verbal argument for the identity in Question 12.
Prove thatA = (\-A,+„)Al-4-A^.-,'A,+„.x:n\
Obtain a formula for the net single premium at age x for an insurance policy which pays 1 at the end of 10 years if death occurs within that period, or at the end of the year of death if death occurs
Assume that a single rate of mortality, q-^+n, is increased to qx+n + k for some constant k. All other values of qy remain unchanged. Show that A^ will be increased by the amount kv^^\px{\ - Ax^n^x).
The net single premium for a pure endowment of 10,000 issued at age X for n years is 8000 if the premium is to be returned in the event of death before age x-\-n. If the premium is not returned, the
Herman, aged 45, purchases a whole life policy of 100,000. Find the net single premium if (a) M45 = 250 and D^s = 520;(b) A^45 = 8000, Z)45 = 520 and / = .04.
Repeat Question 18(a) for a 20-year term insurance policy given Mes = 35 .
Express the net single premium for the following policy, issued to a person aged 30, in terms of commutation functions: 50,000 if death occurs in the next 20 years, 1 00,000 if death occurs in the
Prove each of the following identities:AppendixLO1 Ax = v-dax A- x:n\ (c) Ax:n\ = = vx:n-ax:n\ - = 1 di x - a (d) Ax:n v-A ax:n = x:n+11 d Mx = Dx-dNx 1- ia x:1-11 (g) 1+i MxMx+1+Dx+1 Dx
(a) Find the rate of interest if a;^ = 15.5 and^;^ = .25.(b) Given M^ = 3000, M^+i = 2800 and q, = .01, find D^+i
Ronald, aged 40, purchases a whole life policy paying 10,000 during the next 10 years and 20,000 during the ten years after that.If Ronald is still alive at age 60, he will receive 200 at the end of
Angela, aged 55, purchases a deferred life annuity of 4000 per year commencing at age 65. Before age 65 there is a 10,000 death benefit payable at the end of the year of death. Find the net single
Repeat Question 24 if the life annuity is guaranteed, payable to either Angela or her estate, for 50 years.
(a) Find the net single premium for a 50,000 life insurance policy, payable at the moment of death, to a life aged 40 if it is assumed that / = .06 and iPaq — (.97)' for all t.(b) Do part (a) if
Julio's mortality for 1 < / < 4 is assumed to be governed by the law tPx = -3(4 — /). Harold's mortality for 1 < / < 5 is governed by fp^ = .25(5 — t). If / = .07, find the price at time of an
Prove that ri\Ax\. Give a verbal explanation for this inequality.
A 20-year-old purchases a 100,000 whole life policy with benefit payable at the moment of death. Given d = .05 and fix = .02 for all X, find each of the following:(a) The net single premium for this
Herb purchase a 100,000 whole life insurance policy, with the benefit payable at the moment of death. The policy pays an additional 50,000 if death occurs during the first 5 years due to specified
Assuming a constant force of mortality fi^ and a constant force of interest 6, find n such that A ^-^ = 2A ^-,.
(a) Derive the formula ^ ^;;;;| = 1 — Sa^-, — v^nPx-(b) Derive the formula A^-^ = \ — 6a^-y AppendixLO1
Using integration by parts, derive the formula ^;r = 1 — Sa^.AppendixLO1
Brenda purchases life insurance which will pay 100,000 if she dies during the next 5 years and 200,000 if she dies after that. The benefits are payable at the moment of death. It is known that b —
Helen is informed that the net single premium for 100,000 of whole life insurance, payable at the moment of death, is 65,000. If Helen is subject to a constant force of mortality ^^ = 0275, and if 6
George is informed that the net single premium for a 200,000 whole life insurance policy, payable at the moment of death, is 70,000. If George is subject to a constant force of mortality/ijc = .03,
Do Question 28(a) if we assume the insurance is to be deferred for 20 years.AppendixLO1
Repeat Question 27 if we continue to use (5 = .05 but now assume that the life is subject to a de Moivre's survival function with terminal age 1 10.
Find the price of whole life insurance with a face value of 100,000 sold to a person aged 40 in each of the following cases.(a) /?;, = .96forallxand/=-.09.(b) ix= 1000(^1 - -^\ and/ -.13.
Repeat Question 1 if the payment of 100,000 is to be made at the end of the 5-year period in which death occurs.
Repeat Question 1 if the insurance is a term policy for 30 years.
Repeat Question 1 for 30-year endowment insurance.
Repeat Question 1 if the policy has a face value of 100,000 for the first 30 years only. If the insured survives to age 70, he is paid 70,000 and the remaining 30,000 is retained as a whole life
Repeat Question 1, if in each case, /"^^^^ = . 12, but the benefits are still paid yearly.
Prove that the identity yi' - < ^^^ < A^-\ is true for all x and for all•^ x:n\ ^-"1
(a) Find the price of a 100,000 life insurance policy, payable at the moment of death, bought by a life aged 40 if it is assumed that 6 = .05 and ^x = -04 for all x.(b) Do part (a) if the 40-year-old
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