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.
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If integrated tail $F_I$ is subexponetial, is $F$ also subexponetial?
Im currently reading Non-Life Insurance Mathematics by Thomas Mikosch and in chapter 4 on Ruin theory there is constant distinction between light and heavy-tailed distributions (as there should be) ...
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Help me calculate the assumed interest rate $i'$ under $\frac{\bar{A}_x}{\mu_x}=\bar{a'}_x \neq \bar{a}_x$
Setup
force of mortality $\mu_x = 0.005\cdot (1.01)^x$
original assumed interest rate $i = 0.05$
assumption:
$$
\frac{\bar{A}_x}{\mu_x}=\bar{a'}_x (\neq \bar{a}_x)
$$
At this point, we want to ...
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Probability of the Maximum of $6$ die rolls
Someone please explain to me why this is wrong. Here is the question:
If I roll $6$ different fair $6$-sided dice, what is the probability that the maximum of the rolls is $5$?
My approach was to ...
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Why is $\varphi$ differentiable?
In the proof of a lemma (called the fundamental integral equation for the non-ruin probability) in the book Non-Life Insurance Mathematics by Thomas Mikosch (page 164) we get to the following ...
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Using the critical value from signs test to reject null hypothesis
Question 1
(a) A graduation using $20$ age groups has resulted in $6$ positive and $14$ negative deviations. Carry out the signs test on these data.
(b) A graduation covers $20$ age groups. The number ...
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Why is a factor of 24 used in this Central Limit Theorem Question?
I have a question from Example 12.3.1 from Marcel B. Finan book Lecture Notes in Actuarial Mathematics
Question:
Let $X_i$, $i = 1, 2, \dots, 48$ be independent random variables that are uniformly ...
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Present value involving deferred annuities - is this a typo?
Catfish Hunter’s 1974 baseball contract with the Oakland Athletics called for half of his 100,000 salary to be paid to a life insurance company of his choice for the purchase of a deferred annuity. ...
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Improper Integral $\int_{0}^{\infty} \log(t) t^{-\frac{1}{2}} \exp\left\{-t\right\} dt$
Background
Hi. I am currently writing my undergraduate thesis which mainly revolves around the generalized log-Moyal distribution pioneered by Bhati and Ravi (see here). In the aforementioned article, ...
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What is the difference in the wording of these questions?
Question 1: An account with an initial amount B earns compound interest at an annual effective interest rate $i$. The interest in the third year is $426$ and the discount in the seventh year is $812$. ...
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Question about accumulated values and nominal rates of discount
A collection agency pays a doctor $\$5,000$ for invoices that the doctor hasn't been able to collect on. After two years, the collection agency has collected $\$6,000$ on the invoices. At what nominal ...
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Best books covering SOA Exam Fm
Looking for book recommendations to self learn material for SOA exam FM. (This exam is mostly equations involving compound interest). Particularly something that covers the underlying math intuitively ...
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Thiele differential equation for reserves
I am supposed to solve the below question using Thieles differential equation, and I am having a hard time formulating Thieles differential equation for this specific insurance case and would ...
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How to calculate the accumulated value of a simple interest annuity?
An account is credited interest using 6% simple interest rate from the date of each deposit into > the account. Annual payments of 100 are deposited into the account. Calculate the accumulated
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Calculating the withdrawal amount from a fund as an annuity-immediate incorrectly
I have the following problem.
Consider an investment of $5,000 at 6% convertible semiannually. How much can be withdrawn each
half-year to use up the fund exactly at the end of 20 years?
I can tell ...
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Negative binomial distribution with non integer parameter
I am solving an actuarial math problem.
Suppose that the number of claims, $N$, in a year follows a Poisson distribution $\mathrm{Po}(\Theta)$, where $\Theta$ is a gamma distribution $\Gamma(5, 1/2)$, ...
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