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  1. Linear Exponential Family & Inverse Exponeital Distribution

    Suppose the model distribution X|Λ=λ is inverse exponential
    f(x|λ) = λ exp(-λ/x) / x^2
    and the prior distirbution for Λ is gamma with parameters α and θ.
    (note: this belongs to the case of "exact...
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    Multiple Decrement Insurance: Find Var(Z)

    https://sites.google.com/site/asdfasdf23135/mlc12.JPG

    How can we find Var(Z)? I got completely lost...
    Can someone please explain how to solve this problem?

    I believe E(Z)=APV=300 * (0.8 *...
  3. If we instead assume both independent lives have...

    If we instead assume both independent lives have "constant forces of mortaility", would we be able to calculate A_xy directly?
  4. So do you think the calculation of the APV for a...

    So do you think the calculation of the APV for a DISCRETE joint-life status whole life insurance, A_xy, would be impossible to test on the exam?

    How would a more reasonable problem requiring the...
  5. 1) OK, I see. But in this case for discrete...

    1) OK, I see. But in this case for discrete insurance, shouldn't the upper limit of the sum be 29 (since 30|qxy = 0)??


    2) Let me summarize your assertion as follows:
    If T(x)~uniform,...
  6. Hi and thanks for your reply. ...

    Hi and thanks for your reply.

    https://sites.google.com/site/asdfasdf23135/mlc11.JPG
    1) So should the upper limit of the sum here be 29, 30, 34, or 35? How can we figure this out?? I seem to be...
  7. Calculate Discrete Joint-Life Insurance under DML......

    Consider two independent lives (65) and (70).
    You are given:
    i=0.05
    μ(65+t) = 1/(35-t)
    μ(70+t) = 1/(30-t)
    (so both lives are DML with ω=100).
    Calculate A_65:70. (discrete joint-life status...
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    I've corrected the typo in the solution, the...

    I've corrected the typo in the solution, the correct answer should be 2.218<P<3.551, I'm sorry.


    And yes, this was exactly where I got confused before.
    I think the key thing is to distinguish...
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    Find the no arbitrage "Bounds"

    The stock of a company is trading at $103. A 3-month call option with a strike price of $90 is trading at $17. You can BORROW money at interest rate 8% and can LEND money at 2%. The risk-free...
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    Recursion: u(x) = c(x) + d(x) u(x+1)

    You are given:
    (i) u(x) = (i/δ) v q_x + v p_x u(x+1) for x=0,1,2,...
    (ii) u(80)=0
    (iii) Deaths are uniformly distributed within each year of age.
    Express u(40) as an insurance of the appropriate...
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    But at the bottom we have the APV for an n-year...

    But at the bottom we have the APV for an n-year temporary LIFE annuity, so I believe the premium will be paid for AT MOST n years contingent on survival.
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    In the normal table provided with the SOA exam,...

    In the normal table provided with the SOA exam, we are actually explicitly asked to use the continuity correction when approximating a DISCRETE r.v. with normal distribution. In question 2 above,...
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    APV of premiums & Benefit premiums

    1) For a special fully discrete whole life insurance of 1000 issued on the life of (75), increasing premiums, Q_k, are payable at time k, for k=0,1,2,... You are given:
    (i) Q_k=Q_o * (1+i)^k
    (ii)...
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    2,486

    Percentile Premiums

    1) When a question refers to "percentile premiums", it often will be saying things like "find the smallest annual premium P such that the insurer's probability of a positive financial loss is at most...
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    1) "The company also has the option of a 6.0% one...

    1) "The company also has the option of a 6.0% one year zero-coupon bond starting at time 1. In order to obtain this bond you would have to pay 3% of it's purchase price at time 0." <-------I don't...
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    That is the whole question I got yesterday from...

    That is the whole question I got yesterday from some internet site.
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    1,460

    Asset-Liability matching with the least cost

    If a company has two liabilities (25,000 due at time 1 and 20,000 due at time 2), which of the following combination of bonds satisfies the liabilities and costs the least at time 0? What is the...
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    I am wondering about this too: Is there any...

    I am wondering about this too:

    Is there any difference in 'I short an asset' and 'I sell a stock short' ???
  19. Under compound interest, why is the accrued...

    Under compound interest, why is the accrued coupon not Fr/[(1+j)^(1-t)] ?? (i.e. shouldn't we simply be discounting the amount Fr from time 1 to time t using compound interest?)
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    Thanks! Do you happen to know whether this...

    Thanks!
    Do you happen to know whether this topic is discussed in the other reference textbooks that were on the syllabus?
  21. Bond price b/w coupon dates (accrued coupon based on compound interest)

    F=face amount/par value
    r=coupon rate per coupon period
    j=effective yield rate per coupon period

    Market price = Purchase price - Accrued coupon = P_o (1+j)^t - t * Fr
    where t=number of days...
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    Under which section of the ASM manual does it...

    Under which section of the ASM manual does it correspond to the Brovermanís text Section 5.3.3? That section talks about the Yield on a fund where deposits and withdrawals are made continuously and...
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    TI-30XS Multiview calculator

    For the TI-30XS Multiview calculator, is there any way to put commas in between a large number? i.e. 1,000,000 (as opposed to 1000000)?
    I know this can be done with the BAII+, but can it be done...
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    2,515

    Yes. y+z = .375 x+z = .25 So x+y+2z=0.625...

    Yes.

    y+z = .375
    x+z = .25

    So x+y+2z=0.625
    =>2z=0
    =>z=0

    So I think the answer is indeed 0.
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    Law of total probability

    An insurance company offers one of the following choices to each of their employees:
    (i) Take exactly two insurances
    (ii) Take no insurance but get a lump sum of money
    The probability of having...
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