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.

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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 ...
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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 ...
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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 ...
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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, ...
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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 \...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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(...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: $S = X_1 + ... + X_n$ ...
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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.
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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 ...
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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 ...
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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 ...
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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 $Z_t=\displaystyle\sum_{i=0}^{N_t} X_i$, ...
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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 ...
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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 ...
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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=\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...