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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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Understand $PV^{e;n}=e^{-rn}I_n$, a n-year pure endowment

I am taking a course in basic life insurance, and we use this book. If you look at the bottom of page 40, they have this term called a pure endowment insurance, where it states that its present value at time 0 is: $$PV^{e;n}=e^{-rn}I_n,$$ I really…
Frederik
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Finding PV with multiple interest rates....

I've looked for a question that hits on something similar without success. The problem is this: at time 10, an asset pays 1000. Then the teacher gave us a bunch of random interest rates for times 0 to 2, 2 to 5, 5 to 8, and 8 and beyond. I'm…
ravenclawmathboy
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In select mortality tables (assuming a 3-year select period), why is $\ell_{x+3}$ written without braces around the x?

I am currently referring to Life Contingencies by C. W. Jordan, which gives the following reason: "The select symbol $[x]$ is not used in the $\ell_{x+3}$ column, since the effects of selection do not carry over into the fourth year, and…
Joel Khoo
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age-to-age paid loss development and age-to-ult factors

I am studying ultimate claims. There it shows how to calculate the age-to-age paid loss-development factors by looking at the previous year claims amounts and their cumulative of claims to date. Then they magically use age-to-ult factor and multiply…
kronos
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Tenant wants to pay future rent

The rent of a house is $1500 p.a. payable quarterly in arrear. The tenant wishes to pay a sum now to dispense with the payment of rent in the 4th, 5th, 6th and 9th years. What should the sum be if the interest rate is 4% p.a effective. is 4% p.a.…
user545637
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2 methods to calcuate Sx(t)

I just began studying for the SOA LTAM exam. There are 2 methods shown in the text for calculating $S_x(t)$, the survival function for a life age x to survive until at least time t: Method 1: $S_x(t) = \frac{S_o(x+t)}{S_o(x)}$ Method 2: $$Sx(t)…
user221943
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Multiple State Model : transition probability when state 0 can be re-entered

In a multiple state model, where transition intensities are constant throughout the year : force of transition from state 0 to 1 = 0.05, force of transition from state 1 to 0 = 0.08, force of transition from state 1 to 2 = 0.15 I am asked to verify…
Ck Law
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Finding the new base value of a bond when changing yield rate

A 20000 bond has annual coupons and is redeemable at the end of fourteen years for 22600. It has a base amount equal to 18450 when purchased to yield 6%. Find its base amount if it were purchased to yield 7%. I assumed that both bonds would have the…
B. Houha
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Are these expressions, for the EPV of a benefit paid by an insurance policy, equivalent?

The following screenshot shows part of the provided lecture notes for a module on actuarial mathematics: My question is as follows: is this equation equivalent to simply writing $$ \bar{A}_x^{ik} = \int_0^\infty e^{-\delta t} {}_t p_x^{ik}…
M Smith
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Help with accuracy: The first payment will be made in exactly one month. The effective annual rate of interest is 8 %. Determine the value of X

Betty received $ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly…
IanWalter
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How much should they deposit to reach their goal?

Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is 5 into an ordinary annuity earning 7.04% and they calculate that they will…
EvanSwan92
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Where have I gone wrong? Compound interest

Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 12500 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and…
EvanSwan92
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Finding accumulated amount with rate of discount

I'm struggling with the following questions. A sum of £1000 is invested in an interest bearing bank account. Determine the accumulation of the account over 5 years and 4 months if: $d^{3} = 6.5$% per annum. where d represents the rate of discount to…
alpha787
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Annual effective rate of interest

Galileo deposits 15,000 in a bank. During the first year, the bank credits an annual effective rate of interest i. For the second year, the bank credits an annual effective rate of interest (i-5%). At the end of two years, he has 18,093.75 in…
Mohd Shahril
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Question on life tables with application to multiplication rule

You are given $_5p_{40}=0.8, _{10}p_{45}=0.6,_{10}p_{55}=0.4$. Find the probability that $(40)$ will die between between the ages of $55$ and…
Tosh
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