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

Abstract 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.

[1]  Robert M. Mnatsakanov,et al.  Recovery of a quantile function from moments , 2017, J. Comput. Appl. Math..

[2]  Robert Kast,et al.  A Value at Risk Approach to Background Risk , 2001 .

[3]  Florin Avram,et al.  On the efficient evaluation of ruin probabilities for completely monotone claim distributions , 2010, J. Comput. Appl. Math..

[4]  A. Kyprianou.  Fluctuations of Lévy Processes with Applications , 2014 .

[5]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[6]  Artak Hakobyan,et al.  Approximation of the ruin probability using the scaled Laplace transform inversion , 2015, Appl. Math. Comput..

[7]  Robert Sollis.  Value at risk: a critical overview , 2009 .

[8]  Thorsten Rheinländer.  Risk Management: Value at Risk and Beyond , 2003 .

[9]  Henryk Gzyl,et al.  Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments , 2013 .

[10]  Claudia Klüppelberg,et al.  Operational VaR: a closed-form approximation , 2005 .

[11]  Robert M. Mnatsakanov,et al.  A note on recovering the distributions from exponential moments , 2013, Appl. Math. Comput..

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 2 , 1967 .

[13]  Javier Cárcamo,et al.  On uniform approximation by some classical Bernstein-type operators☆ , 2003 .

[14]  Michel Denuit,et al.  Properties of a Risk Measure Derived from Ruin Theory , 2011 .

[15]  Philip J. Boland.  Statistical and Probabilistic Methods in Actuarial Science , 2007 .

[16]  J. Abate,et al.  Multi‐precision Laplace transform inversion , 2004 .