# Some Maple applications to risk theory models

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Risk theory considers stochastic models that may be used to study the risk of a risk enterprise, where the nature of the operation is such that expenditures may exceed receipts during some accounting periods in the normal course of operation. This dissertation begins with a discussion of the classical risk model, the probability of ruin, some specific examples of how the probability of ruin can be computed for given claims distributions, and premium calculation principles. We also examined how the probability of ruin can be approximated using the Cramer-Lundberg approximation. Additionally, we present how the Laplace transform can be used to solve the integro-differential equation for the probability of ruin. Finally, we give specific examples on how Maple can be used in risk theory computations. The modified Bessel function is used in computing probabilities related to the sum of claims process. The Cramer-Lundberg approximation for the probability of ruin is computed, under specific claims distributions. Finally, Maple was used to compute the probability of ruin for various claims distributions using elimination of integral technique and for other distributions using Laplace transforms.