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Theoretical aspects and simulation of a generalized surplus process with a logarithmic barrier. (English) Zbl 1199.91096

Summary: In this article we consider a generalization of the classical Lundberg surplus process. In the presence of the logarithmic dividend barrier we assume that the company also receives interest on its reserve with a constant interest rate. We derive equations for the survival probability and the expected sum of discounted dividend payments. We give important theoretical results concerning the existence and uniqueness of the corresponding solutions. We use Monte Carlo (MC), quasi-Monte Carlo (QMC) techniques and the direct simulation approach in order to estimate these quantities. We also perform numerical tests, in which we compare the accuracy of these algorithms.

MSC:

91B30 Risk theory, insurance (MSC2010)
65C05 Monte Carlo methods
91G60 Numerical methods (including Monte Carlo methods)
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