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.
31
questions
0
votes
0answers
7 views
Cramer Lundberg risk model
I am trying to apply this model real situation. I can not understand the premium rate. I know the model, that is
Y_t=r_0 + ct- \sum{X_i}.
What is the premium rate c?
Is the rate or percentage of what ...
0
votes
1answer
22 views
Inferring properties of the sum of R.V.s from the copula
This is not a completely well defined question, so even help making it coherent will be useful.
Setting: Suppose I know the marginal distributions of random variables describing the expected losses ...
0
votes
1answer
29 views
calculate survival probability and expected payout
I have data taken from here. Let us look at one specific column qx for female up to the age of 10. qx represents the mortality rate between age x and (x+1), that is the probability that a person aged ...
3
votes
4answers
205 views
Covid-19 and life expectancy
A public figure in my home country said the following:
"The life expectancy in our country is 82 years. The average age of those who die of covid-19 is also about 82 years. Hence, on average, ...
0
votes
0answers
32 views
Hilbert space of random VECTORS?
I'm trying to break through H. Buehlmann and Gisler's Cource in credibility theory. At the page 183 they write that we have to show that
$$ \boldsymbol \mu (\Theta_i)-\widehat{\widehat {\boldsymbol \...
1
vote
1answer
22 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
139 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
34 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
82 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-...
1
vote
0answers
37 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
1answer
41 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
55 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(...
1
vote
1answer
32 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
164 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
12 views
Remediation for distributions with infinite moments [closed]
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
128 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
106 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
52 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
1k 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
1k 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
847 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
645 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
117 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$$
Where $Z_t$ is a compound Poisson sum, it means that $Z_t=\displaystyle\sum_{i=0}^{N_t} X_i$, ...
2
votes
1answer
180 views
Modeling bimodal time-to-event
Here is a plot of death registration frequencies by age for the UK in 1974.
I see distributions like this quite often: there is some event (e.g. death) which happens either close to birth, or ...
0
votes
1answer
717 views
Compound Poisson Process with Weibull jumps
I need to simulate a compound Poisson Process in R, however I am not clear with the algorithm to generate it. I have conceptual gaps.
I know by definition that:
A compound Poisson process is the ...
1
vote
0answers
116 views
Monte Carlo approach in a distribution of a loss process
I am trying to estimate the next quantity using Monte Carlo method.
I have the next well-known quantity called the Crámer-Lundberg risk process, given by the expression
$$Y_t=x+ct-Z_t$$
where $Z_t=\...
0
votes
2answers
82 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
45 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
232 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 ...
