Questions tagged [actuarial-science]
Questions relating to financial risk; often, but not limited to, insurance. This includes questions regarding stochastic distribution of cash flows, probability of ruin, financial payments above a threshold, etc.
28
questions
1
vote
1answer
16 views
Independence of censoring time $C$ and event time $T$ for randomised entry to a study
While reading through the textbook 'Modern Applied Statistics With S' by Venables and Ripley, I came across the following paragraph detailing the different types of censoring possible when dealing ...
0
votes
0answers
35 views
solvency capital requirement using copulas in R
I want to prove that using copulas the SCR for solvency 2 can be lower than using the standard formula. In the following code I simulate three different distributions, I calculate the scr and then I ...
0
votes
0answers
31 views
Estimating coefficients of a large categorical variable
I'm trying to fit a GLM model with a categorical variable with 400 categories, and I'd like to reduce the number of categories. There are some categories with a lot of data, and a lot of categories ...
2
votes
1answer
60 views
Do good Cross-Validation results imply good QQ-plot results?
In Edward Frees' book Predictive Modeling Applications in Actuarial Science, Volume 2 the first chapter goes over how to build a frequency GLM model (using a Poisson distribution) on sample auto-...
0
votes
0answers
17 views
Question on variance on finding the variance
I have a question on finding the variance of the giving problem:
On an auto collision coverage, there are two classes of policyholders, A and B. 60% of drivers are in class A and 40% in class B. The ...
1
vote
0answers
24 views
Hazard rate from Weibull vs. cumulative hazard plot does not match
)
My problem is that I have HR for a factor named "Selvrisiko" and I get the
output estimates (HR) (Upper bound) (Lower bound) as:
but when I plot (Kaplan - Meier) cumulative hazard for the ...
0
votes
0answers
17 views
Net Premium Formula
I need to explain the following algorithm of the calculation of net premium.
Let $S_i$ be a total insurance amounts per year $i$ and $S_{b,i}$ is a total loss per year $i$. Then
$$
y_i=\frac{S_{b,i}}{...
0
votes
1answer
39 views
Obvious demonstration of the posterior density of normal laws in bayesian inference
Given the observations' density $f(X|\theta) = \mathcal{N}(\theta,1)$ and the prior density $f(\theta) = \mathcal{N}(0,\sigma^2)$, it it is said that it is obvious that the posterior density is equal ...
2
votes
0answers
46 views
Lee Carter mortality model - OLS (SVD) estimators if errors are heteroscedastic
In the classical Lee-Carter model, central death rates are modelled as follows:
$\log(m(x,t)) = a(x) + b(x)\kappa(t) +\varepsilon(x,t)$
for some $x=0,\ldots,\omega$ and $t=1,\ldots, T$ and where $a(...
0
votes
1answer
27 views
Calculate $\mathbb{P}[Y=y|X=x]$ where $X$=# claims reported diring firs year, $Y$=# claims that will eventually be reported
A property-casualty insurance company issues automobile policies
on a calendar year basis only. Let $X$ be a random variable
representing the number of accident claims reported during calendar
year ...
1
vote
1answer
104 views
Copula partial derivates
I have some troubles with the demonstration of this theorem:
Let C be a copula, for any v in I=[0,1] the partial derivative for u exists for almost (Lebesgue meaning) all u, and it is included between ...
1
vote
0answers
10 views
Remediation for distributions with infinite moments
A colleague of mine posed a question to me regarding certain distributions used in loss models. Naturally occurring distributions, such as inverse Pareto, do not have finite moments. But naturally ...
1
vote
0answers
94 views
R - matrix optimization problem (Lee-Carter with MLE parameters)
I am trying to reproduce one of models evolved on the base of Lee-Carter model by use of RStudio. Because I am still pretty fresh in this software, my question is not really sophisticated.
Applying ...
5
votes
1answer
85 views
Basic calculations with Order Statistics
I've come across the following problem, and I am tempted to delve into order statistics to solve this. I would greatly appreciate any help!
Suppose you draw 6 independent samples from a continuous ...
0
votes
1answer
34 views
Compound risk poisson models
I was just working through this question.
A compound Poisson risk model is used to model the total claims S
experienced by an insurance company over one year, of the form:
$S = X_1 + ... + X_n$
...
-1
votes
1answer
793 views
Is Maximum Likelihood Estimation the median? [closed]
I asked what maximum likelihood estimation to a friend of mine. He told me that it is the median which I don't understand.
1
vote
2answers
648 views
Attempting to find mean of Weibull function in R
I am using a Weibull distribution in R, and know that:
E(X) = 1000 and Var(X) = 500,000
Knowing:
E(X^r) = ($\Gamma$(1+ (r/$\gamma$))) * 1/c^(r/$\gamma$))
I ...
1
vote
0answers
624 views
How to calculate life expectancy of the astronauts?
I'm trying to obtain a more authoritative answer to the question: Do astronauts live longer than earthlings?
While the time dilation thing has been easily dismissed as it introduces negligible ...
0
votes
1answer
500 views
model for pure premium using GLM for frequency and severity [closed]
I want to estimate a model for frequency and for severity in order to obtain a pure premium, defined as frequency by severity.
The frequency is calculated as claim count divided by exposures, this ...
0
votes
0answers
90 views
Maximal aggregate loss in Risk Process
I am studying the Crámer Lundberg Risk Process. This process is defined as follows:
$$Y_t=r_0+ct-Z_t$$
Where $Z_t$ is a compound Poisson sum, it means that $Z_t=\displaystyle\sum_{i=0}^{N_t} X_i$, ...
2
votes
1answer
127 views
Modeling bimodal time-to-event
Here is a plot of death registration frequencies by age for the UK in 1974.
I see distributions like this quite often: there is some event (e.g. death) which happens either close to birth, or ...
0
votes
1answer
508 views
Compound Poisson Process with Weibull jumps
I need to simulate a compound Poisson Process in R, however I am not clear with the algorithm to generate it. I have conceptual gaps.
I know by definition that:
A compound Poisson process is the ...
1
vote
0answers
108 views
Monte Carlo approach in a distribution of a loss process
I am trying to estimate the next quantity using Monte Carlo method.
I have the next well-known quantity called the Crámer-Lundberg risk process, given by the expression
$$Y_t=x+ct-Z_t$$
where $Z_t=\...
0
votes
2answers
47 views
Correlation Between Years for Similar Population
A common problem in insurance is to predict the amount (number, severity, or aggregate total) of losses in the next year for a book of business (eg. all personal auto policies). To do this, one can ...
2
votes
1answer
40 views
What are good resources on nonlife actuarial science as it is being applied in industry?
I have already browsed my way through the book Nonlife Actuarial Models: Theory, Methods and Evaluation by Yiu-Kuen Tse and I am already familiar with nearly all of the underlying statistics in that ...
1
vote
0answers
55 views
What to do when you don't have a lot of data?
I understand that there won't necessarily be a great answer to this, but I'd like to hear what people would do in this situation.
Here's the data situation: I have about 30K policy records of which ...
1
vote
2answers
3k views
What books are good for exam p for actuarial science
Hello I'm going to be a sophomore in college and planning on taking exam P for actuarial science. One of my weakest topic is probability. What "entry level" book would you recommend before I start ...
1
vote
1answer
208 views
Is there a Poisson-Gamma-Gamma model?
An example to elucidate my problem: The total claim amount can be modelled by a Poisson-Gamma model as it is assumed that the events (e.g. accidents) are Poisson distributed and the claims are Gamma ...
