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