Expected discounted penalty function and asymptotic dependence of the severity of ruin and surplus prior to ruin for two-sided Lévy risk processes

On the Expected Discounted Penalty Function Using Physics-Informed Neural Network

“…Preischl and Tonhauser [7] minimized expected discounted penalty functions in a Cramér-Lundberg model by choosing optimal reinsurance, showed the existence and uniqueness of the solution found by this method, and provided numerical examples involving lightand heavy-tailed claims. Martin-González and Kolkovska [8] studied a generalization of the expected discounted penalty function for a class of two-sided jump Lévy processes having positive jumps with a rational Laplace transform and provided an explicit expression for the generalized function in terms of functions depending only on the parameters of the Lévy process. Te expected discounted penalty function provides a unifed framework for the evaluation of various risk quantities.…”

“…Te expected discounted penalty function provides a unifed framework for the evaluation of various risk quantities. For a systematic study of the Gerber-Shiu theory, one can refer to references [1][2][3][7][8][9][10][11][12].…”

“…Although the expected discounted penalty function was proposed more than two decades ago and continues to play an important role in actuarial science research, there are still many unsolved problems such as the two here for generalizing the discount rate in this function from a constant to a random variable for the nonclassical risk model and looking for an efective numerical scheme for this function with no explicit solution (see [3,[5][6][7][8][9][10][11][12]).…”