Προσεγγίσεις κατανομών πιθανότητας από μία μείξη εκθετικών κατανομών
Approximations of probability distributions by mixtures of exponentials
SubjectΑσφάλιση -- Μαθηματικά ; Μαθηματικά των επιχειρήσεων ; Insurance -- Mathematics ; Business mathematics
In actuarial science and more specifically in ruin theory, it is important to calculate the ruin probability (the calculation of the probability company's surplus gets a negative value). Long tail distributions are among the most studied claim amount distributions. Nevertheless, the calculation of ruin probability in these distributions faces difficulties. A case where this probability can be easily calculated is when the claim amount distribution is a mixture of exponential distributions. In the current dissertation we will mainly focus on the approximations of probability distributions by mixtures of exponentials. This will allow us to calculate approximately the ruin probability of various continuous random variables which follow distributions with long tail.