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Questions tagged [actuarial-science]

Actuarial science is a discipline that uses mathematics and statistics to assess risk. The mathematics involved in actuarial science includes probability, statistics, finance, life insurance mathematics, and more.

Actuarial science is a discipline that uses mathematics and statistics to assess risk. The mathematics involved in actuarial science includes probability, statistics, finance, life insurance mathematics, computer science and more.

Originally, actual science used deterministic models in the construction of tables and premiums. It has gone through revolutionary changes since the proliferation of high-speed computers and the union of stochastic actuarial models with modern financial theory.

To be used with more specific tags, such as , and . See https://en.wikipedia.org/wiki/Actuarial_science for more information.

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annuity- find the present value of varying payments

I am trying to find the present value of an annuity, where we have a $20$-year annuity immediate where the first payment is $1000$, and each subsequent payment is increased by either $50$ for the first $10$ payments or by $100$ for the last $10$…
comp890
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Using accumulated value to match present value of future payments

Question: Ms.Smith has two grand children, Adam and Evelyn. Adam will begin college on 9/1/03 and Evelyn will start college on 9/1/05. Ms.Smith wants both Adam and Evelyn to receive $1,000 at the beginning of each of their 4 years in…
swordlordswamplord
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Present value of deferred life annuity-due

Kimberly is told that she can receive a 250,000 death benefit from her husband's life insurance in annual installments of 25,000 at the beginning of each year for 11 years and a final payment of 16,265 at the beginning of the 12th…
swordlordswamplord
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Using goal seek in excel.

Hi I don't know if this is an appropriate question for this page but I thought it was worth a shot and if nothing else a learning experience. So I am studying actuarial mathematics and I am currently working on problem involving calculating the…
user848643
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Cash flows using bond investment to balance liabilities

An insurance company must pay liabilities of 99 at end of year 1, 102 at end of year 2, and 100 at end of year 3. The only investments available to the company are the following 3 bonds. Bond A - 1 year to maturity, yield rate 6% coupon rate 7% Bond…
swordlordswamplord
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price of two bonds given the period, par value and coupon being (i + 0.04) and (i - 0.04) and that one bond is x amount greater than the other

Given the following determine the price of each bond and the yield rate i. i- each bond is 10-year bond with semiannual coupons redeemable at its par value 10,000 and is bought to yield an annual nominal rate i, convertible semi-annually. ii- bond A…
swordlordswamplord
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Formula for decreasing annuity by k% every year

Lets say you have an annuity where you make annual deposits for n years, with the first payment being x. Then each subsequent deposits is k% smaller than the previous. And you are given the effective annual interest rate i%. How do you find the…
user520403
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How do I evaluate a geometric progression that is decreasing?

Given the following 4 characteristics determine the loan amount. First payment of $2000 due one year from now. Next 7 payments are 3% larger than the preceding payments. Next 7 payments are 3% lower than the preceding payments. Loan has annual…
swordlordswamplord
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Macaulay Duration

Consider two bonds purchased at the redemption value of 1000, and due in 5 years. One bond has 5% annual coupon rate payable semi-annually and the other has 10% annual coupon rate payable semi-annually. Find the duration of each bond if both bonds…
swordlordswamplord
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Perpetuity formula

I got this question and I don't understand how to go about it: If someone makes a deposit of 200 dollars at the end of every month in an account earning interest $i^{(12)}=0.072$ to fund a perpetuity with monthly payment of 480 starting 1 month…
user520403
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Given delta t and its domain, find accumulated value of annuity n periods later.

Find s5 if δt = 0.02t for 0 ≤ t ≤ 5. https://i.stack.imgur.com/7Yw72.jpg My answer sheet gives me 5.7726 and I don't know how it got that answer. Can someone please explain how my method is incorrect? I was asked to find the accumulated value of an…
swordlordswamplord
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Poisson modelling of log normal claims for non life insurance

Suppose we have a portfolio of $J = 1000$ policies. Assume further that the number of claims $N$ is Poisson distributed with intensity $µ = 0.01$, and that the claim sizes $Z_i$ follow a log-normal distribution with $\mathbb{E}(Z_i) = 2$ and…
Jonathan Kiersch
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Certainty equivalent related to the net present value when there is no interest

Throughout we work with the assumption that there is no force of interest (i.e. the interest rate is $i=1$). Consider a lottery $X$ that pays $1000$ with probability $e^{-1}$ and $0$ otherwise. Then its expected net present value is $1000e^{-1} +…
DesmondMiles
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Financial Appraisal - Discounting

Suppose we were given a discounted cost of $50,000, which has been generated using a discount factor of 3.5% and a time-horizon of 45 years. Is it possible to obtain what the non-discounted cost is today? For clarity, this is not as part of a…
EB3112
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stop loss ordering of risks

I am working through the textbook "Modern Actuarial Risk Theory" and came across the part where stop loss orders are introduced. It is defined as $X<_{SL}Y \iff E[(X-d)_{+}] <= E[(Y-d)_{+}], d\geq0$. Now let X,Z be two risks with $X<_{SL}Z$, define…
Randomuser
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