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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Closed form for Exponential Conditional Expected Value & Variance
I am wondering if there is a closed form for finding the expected value or variance for a conditional exponential distribution.
For example:
$$ E(X|x > a) $$ where X is exponential with mean ...
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1answer
38 views
Probability of $X^{2} > Y^{3}$ over distribution other than uniform
I was working on a problem in which $X$ and $Y$ are continuous random variables which both have the uniform distribution $U[0, 1]$.
The question was: what is the probability that $X^2 > Y^3$.
...
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0answers
18 views
I have R-CODE for coumpute run off triangle in IBNR(method of simulation) [closed]
I have R-CODE for compute run off triangle in IBNR ; I know ,it have cran in R but i want R-CODE .
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1answer
71 views
Bonds and Force of Interest
Studying for FM/2 and ran into this problem dealing with bonds;
A 1,000 par value 3 year bond with annual coupons of 50 for the first year, 70 for the second year, and 90 for the third year is bought ...
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2answers
64 views
Finding moment generating function from piecewise CDF
I am stuck on this problem:
I am given the CDF, and unless there is a shortcut I am not remembering, I need to find the PDF before I can get the moment generating function and solve the problem.
...
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2answers
59 views
Probability of being within one standard deviation of mean given only a moment generating function
I am trying to figure out how to approach this:
For starters, I calculated M'(0) and M"(0), which allowed me to find the mean and variance. I got 2 for the mean and 1.6 for the variance. But now, ...
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8answers
20k views
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. ...
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1answer
74 views
Increasing and decreasing annuity
Going in circles.....
Find an expression for the present value of an annuity-immediate where payments start at 1, increase by 1 each period up to a payment of $n$, and then decrease by 1 each period ...
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1answer
36 views
Continuous annuity calculation
This is a problem from Marcel Finan's Exam FM/2 course. It is not homework but I am studying for the FM exam and trying to get through this.
You are given $\frac{d}{dt}\bar{s}_t$ = $(1.02)^{2t}$. ...
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1answer
75 views
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 ...
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1answer
56 views
$e^{F(x,y)}$ Type Multi-variable Exponential Integrals
I am sure all you integration buffs can do this faster than I can type it. Your help with a quick explanation and solution is appreciated.
$$F _{XY} = \int_0^\infty\int_0^\infty xye^{-\frac{x^2 + ...
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1answer
33 views
Stuck on solving for x in exponential to find variance
The problem seems simple:
Let X be an exponential random variable such that $P(X \le 2) = 2P(X > 4)$.
Find the variance of X.
Easy, right?
$
P(x \le 2) = 1 - e^{-2\lambda} $
and
$ P(x > 4) = ...
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1answer
82 views
Procedure for Max Function with identical random variables
I am studying for the P/1 actuarial exam, and I keep encountering one type of problem which I can't seem to solve and can't seem to find any generalized explanation for how to do it in my textbooks. ...
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1answer
378 views
How to convert interest rate to discount factor
I'm studying on Kellison's Theory of Interest and I'm stuck on the exercise 20/a of the 1st chapter.
If the $i=0.1$ then $d = 0.0901$
$d_5=\frac{A_5-A_4}{A_5}$
when I insert $d$ into this ...
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2answers
63 views
Where is the logic with this trinomial probability?
I am studying for Exam P to take in a few hours so I'd appreciate very much if someone got to me befoe I left. The problem says that we have three categories of risk, high, medium and low risk. The ...
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1answer
63 views
Monthly rental fee to achieve given profit on average, given probabilities of numbers of rentals
I have this problem here and I'm very unsure of how to start this. I have an idea but I'm not sure where to go from a certain point. The problem says: A video rental store is analyzing a flat fee ...
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2answers
65 views
Are waiting times always going to be exponentially distributed?
I'm studying for CAS/SOA Exam P/1 and a question I have here is:
We have a portfolio of $20$ insurance policies. The number of claims per policy in a $3$-month period has a Poisson distribution ...
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0answers
164 views
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 ...
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1answer
65 views
Question about polynomials in actuarial science
I'm reading Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 and have resolved my difficulty with one of his questions ...
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1answer
155 views
What does it mean that the probability density function is proportional to a function?
I'm studying for SOA/CAS Exam P and I have a problem that says that $X$ is a continuous and positive random variable whose probability density function is proportional to: $$\frac{1}{(1+x)^5}$$ Where ...
2
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2answers
82 views
Two questions on nominal rates of interest
I'm reading Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 and have difficulty with two of his questions.
Problem 9.6 ...
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1answer
40 views
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 ...
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0answers
46 views
Finding ratio of interest rates
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 ...
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0answers
37 views
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 ...
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1answer
59 views
A question in Finan's FM/2 book
Problem 6 on page 47 of Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 is:
Fund A is invested at an effective annual ...
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0answers
45 views
Simple insurance firm model.
This question is a part of an larger question in actuarial mathematics. It is a model of an insurance firm with periodic stochastic outflows of $X_i$, an initial wealth of u and some income paid ...
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3answers
114 views
SOA/CAS Exam P Question (from previous exam (Nov. '09)): Finding percentiles
So this question comes from SOA/CAS Exam P of November 2009, I'm not sure why the solution is the way it is. The question says this:
An insurance company sells an auto insurance policy that ...
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1answer
100 views
Actuarial / Modelling question - difference between RUN date and VAL date
My understanding is that RUN date is the date you do the RUN (eg in prophet / moses / igloo / whatever, the date on which you performed the calculations)
Whereas VALuation date is the initial 'as at' ...
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2answers
47 views
How would I determine whether these events are independent?
I'm studying for CAS/SOA Exam 1/P and I'm stumped on this question. It says:
From the set of families with two children a family is selected at random. Let $X_1=1$ if the first child of the family ...
4
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3answers
126 views
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 ...
2
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1answer
75 views
How is this the right answer?
In a survey of customer satisfaction, participants are asked to give a score of 1,2,3 or 4 to each of the 6 questions. If participants are instructed not to give the same numerical score to more than ...
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1answer
105 views
Derivation of formula for continues annuities
I'm currently working through a book on the Theory of Interest. Currently, I'm looking at continuous annuities, or annuities that are paid continuously. The book gives the following formula, the ...
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1answer
171 views
Converting an Annuity due to Annuity immediate
I'm working on the following problem at the moment while preparing for an exam.
Find the present value of payments of 200 every six months starting immediately and continuing through four years from ...
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1answer
378 views
Confused about Effective Rate of Discount- Theory of Interest
I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
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1answer
108 views
Help understanding confusing present value question (Theory of Interest)
I'm currently enrolled in a theory of interest class that covers the same material that's on exam 2/FM. At the instructors recommendation, I'm working through all of the problems in the book on my own ...
2
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3answers
170 views
Expected value and life
Let $e_{x} = \int_{0}^{\infty} p_{x}(t) \ dt$ where $p_{x}(t)$ is the probability that a person aged $x$ will survive at least $t$ more years. Why is $e_{x} \leq e_{x+1}+1$?
We know that $e_{x} \geq ...
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3answers
1k views
Masters in Actuarial Science
I am applying to a grad school for the Masters in Actuarial Science. Now i am getting cold feet.
I do love math, i was always good in math (not excellent or a genius). Did all adv. calculus classes ...
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4answers
8k views
Are the actuarial exams hard? [closed]
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. ...
