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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.

641 questions
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Difference between annual net premium and face amount.

I am doing the revision, and confusing about the face amount, net single premium and annual net premium. As I know the net single premium is the present value of the lump sum pay at time 0. How about the annual net premium and face amount? For a…
Jessica J
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Relationship between insurance premium and portfolio size

How would actuarial science refer to the idea that the premium should increase as number of insured entities decreases. In other words, what is the technical term for the intuition that I would charge a higher premium per car to insure just one car…
tapdancer
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calculate the OB using prospective method

I'm learning about the prospective for loan repayment but I'm having trouble creating the equation. Here was my problem (loan repayment- finding the loan if end payment increases by certain amount) I'm finding the outstanding balance after the…
comp890
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How to find the present value of an annuity-due after a certain period p while interest also varies for each year t

Given: i) X is the current value at the end of year two of a 20-year annuity-due of 1 per annum. ii) The annual effective rate for year t is: $$i_t = \frac {1}{8+t}$$ Calculate X. $$ a(t) = (1+i_t) = \frac {9+t}{8+t}$$ From this point, I honestly…
swordlordswamplord
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Where am I going wrong; present value annuity

Suppose that an annuity will provide for 20 annual payments of 1440 dollars, with the first payment coming 7 years from now. If the nominal rate of interest is 8.2 percent convertible monthly, what is the present value of the annuity? My…
user520403
  • 459
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Given Present Value of two annuities-due, find annuities-immediate for time period 4n

For convenience I will denote annuities-due as: a"[n] and annuities-immediate as: a'[n] and let C=level payments or contribution. Given: a"[n]=12 and a"[2n]=21 Problem: a'[4n] = ? So if I read the problem correctly, it is ultimately asking for the…
swordlordswamplord
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What is the actuarial present value of a life insurance given in this question?

I need help on approaching a particular question regarding actuarial science. I just need a rough concept on how to do it, so I won't provide any extra data to keep this simple. For these questions, I have built a cohort life expectancy data which…
Wei Shung
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What does it mean for a force of mortality to be continuous and linear

For (x), you are given that $$\mu_x= \begin{cases} 0.01, &\text{if}& x<50\\ 0.02, &\text{if}& x>60\end{cases}$$ and $\mu_x$ is continuous ad linear on [50,60]. Calculate $_{10}p_{55}\\$. Here is part of my solution: Note that $_{10}p_{55}=…
Jonelle Yu
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Prove that deferred continuous annuity has APV: $E(e^{-\int_w^t \delta(s)ds}\int_0^{T-w}e^{-\int_w^{w+t} \delta(s)ds}dt\mathbb I_{T>w})$

I want to prove that deferred continuous annuity has the APV: $$E(e^{-\int_w^t \delta(s)ds}\int_0^{T-w}e^{-\int_w^{w+t} \delta(s)ds}dt\mathbb I_{T>w})$$ $$=E(\int_0^{T-w}e^{-\int_0^{w+t} \delta(s)ds}dt\mathbb I_{T>w})$$ Where $T$ is the lifetime…
Dole
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Exchanging Increasing Annuity Immediate for a Perpetuity

for the most part I understand this question, but i'm missing something. Any help would be appreciated. "Dipper has a 10 year increasing annuity immediate that pays $100 at the end of the first year, $200 at the end of the second year, ... ,…
user601206
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Is an annuity due paid $p$ times per year for $n$ units of time equal to an immediate annuity payable $p$ times per year for $n-1$ units of time $+ 1$

In symbols, my question is asking the following. Let: $a_{\overline{n|}} = {}$ present value of an immediate annuity payable for n units of time $\ddot{a}_{\overline{n|}}^{(p)}={}$present value of an annuity due payable p times per year for n…
YinWai Tse
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Solving for interest rates without a known term in annuity immediate and annuity due

Sylvestre receives an annuity-immediate with monthly payments of 100. Susan receives an annuity-due with annual payments of 1,165 and the same term. The value of Sylvestre’s annuity is 97.09% times the value of Susan’s. So first I set up the system…
B. Houha
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Finding principal on two loans of equal term given different rates and amounts

I'm reading through Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 on my own and am unsure how to proceed with a question (page 103, question 12.4). It is: Brian and…
not William Sealy Gosset
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Two questions about rate of discount

I'm reading through Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 on my own and I want to make sure I understand discounting. To check that I understand it correctly,…
not William Sealy Gosset
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Immunising two liabilities with a single zero-coupon bond

An investment fund has liabilities of £11 million due in 7 years’ time and £8.084 million in 11 years’ time. The manager of the fund will meet the liabilities by investing in zero-coupon bonds. The manager is able to buy zero-coupon bonds for…
A. B.
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