Recovery of ruin probability and Value at Risk from the scaled Laplace transform inversion

In this paper, we propose three modified approximations of the ruin probability and the inverse function of the ruin probability using the inversion of the scaled values of Laplace transform suggested by Mnatsakanov et al. (2015). The problem of evaluating numerically the tail-Value at Risk of an insurance portfolio is also discussed briefly. Performances of the proposed constructions are demonstrated via the graphs and tables using several examples.