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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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How often does it happen that the oldest person alive dies?

Today, we are brought the sad news that Europe's oldest woman died. A little over a week ago the oldest person in the U.S. unfortunately died. Yesterday, the Netherlands' oldest man died peacefully. The Gerontology Research Group keeps records:…
Řídící
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Darth Vader Rule: what is the reason for its name, and a formal proof?

I often hear the term "Darth Vader Rule" when calculating the expected value using the survival function and taking the integral where it is defined. I am not quite sure why it is called that (is it customary?) and I would also like to know a formal…
hyg17
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Can purchase of insurance be justified mathematically?

When I ask people to explain why they buy insurance, I often hear vaguely of "spreading the risk", but I am not actually sure what that means nor if insurance does this. How is an insurance company any different than a casino? In a thought…
Jeff
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Difference between conditional and intersection in probability.

I am having hard time figuring out if it is a conditional probability or an "and" probability under the following types of problems. When a student is absent, the probability of the student being sick is .6 In such a sentence, I am not quite sure…
hyg17
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How do actuaries calculate the premium of catastrophic insurance given the shortage of data?

Since catastrophes seldom happen, there aren't enough data points for meaningful statistical analysis. So, how do actuaries go about doing their calculation for the premium of these kinds of insurance given the lack of data points?
curious
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Calculating a continuously varying, continuously paid annuity

I'm unsure how to calculate a continuously varying, continuously paid annuity. I'll write up my solution (which I suspect is wrong) to one, sample question, and I would greatly appreciate any correction. The question (problem 29.13 on page…
user55618
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Tail Value at Risk of Normal Distribution

For a random variable $X$, Tail-value-at-risk is denoted as $\operatorname{TVaR}_p(X) = \operatorname E(X \mid X>\pi_p) = \dfrac{ \int_{\pi_p}^\infty xf(x) \, dx}{1-F(\pi_p)}$, where $\pi_p=\operatorname{VaR}_p=$ the value-at-risk $=$ the value such…
EllipticalInitial
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Are the actuarial exams hard?

I heard that they are difficult. Is this true? Are they like the qualifying exams in grad school? For example, is the probability exam and the financial math exam comparable to qualifying exams (e.g. needs months and months of study)?
Larry
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Prove that $\dfrac{0.5x^2 + x + 1}{x^2 + x + 1}$ is a strictly decreasing function.

This is part of an actuarial science problem. Unfortunately, the official solution of this problem takes the derivative of $$\dfrac{0.5x^2 + x + 1}{x^2 + x + 1}\text{, } \quad x \geq 0\text{.}$$ and shows that it is always $\leq 0$. However, this…
Clarinetist
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Which methods are used by actuaries in practice?

Recently I read a comment from an actuary that a lot of the math they studied as part of the program they never actually used. I'm not interested in becoming an actuary, but I'm interested in learning more about some of the methods that are commonly…
Antonio2011a
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How to find limits of integration on a convolution of CRVs

In finding the convolution of two independent and continuous random variables, I am struggling with limits of integration. I cannot seem to figure out over what intervals the probability density function $f_{Z}(a) = f_{X+Y}(a)$ breaks out to. The…
Katyjean57
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Why is nominal interest defined the way it is?

So if nominal interest is 12% compounded monthly, it is actually 1% compounded each month. It is not 12% effective year, though it is close (It is 12.7%) So why don't we/they say 1% compounded monthly? Or just use effective yearly rate? Nothing is…
Miranda
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What does 'central exposed to risk' mean?

I am currently going through some actuarial lecture notes which, without definition, use the term 'central exposed to risk', which it denotes by $E_{x,t}^c$. Having googled this term, the most easily understandable explanation of this term seems to…
M Smith
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Chi Square Contingency Table - Formula Derivation

A chi-square distribution is constructed from normal random variables $X_{i=1, \dots ,n}$, each with normal distribution and mean $\mu$ and variance $\sigma^2$. Transforming to standard normal and squaring, i.e.: $$\frac{(X_i -…
Empire
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Claim from an Actuarial Textbook: limits imply the existence of mean and variance

This is from Actuarial Mathematics for Life Contingent Risks, 2nd ed., by Dickson et al. Some definitions (not directly from the book): Definitions/Notation. $T_x$ is defined to be the future lifetime of a life age $x \geq 0$. We also define the…
Clarinetist
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