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.

22 questions
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Effect of two time series over a different one

I have three time series $X_1$, $X_2$ and $Y$. All of them starting from the same date and with the same length. I know that $Y$ contains information of $X_1$, $X_2$ and other variables that I cannot ...
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How to know if there is a difference between two populations or if some feature has influence on a certain response variable Y?

I have a database about claims at auto insurance. I can do the math and get Frequency, Severity, Sinistrality. I need to know if cars with automatic transmission have a higher propensity to accidents ...
21 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 ...
24 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

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 ...
18 views

Survival Model with delayed-entry

I am building a survival model that looks at pending insurance claims at several different moments in time, and predicts when those claims will close. So for any particular claim I may have five ...
54 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 ...
71 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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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: $S = X_1 + ... + X_n$ ...
107 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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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 ...
310 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 ...
263 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 ...
59 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 $Z_t=\displaystyle\sum_{i=0}^{N_t} X_i$, ...
75 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 ...
335 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 ...
93 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=\...
41 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 ...
32 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 ...
54 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 ...