Mathematical and Statistical Methods for Actuarial Sciences and Finance

44 C. Bolanc ́e, M. Guill ́en, and J.P. Nielsen with the g-and-h distribution, like Dutta and Perry [10] for operation risk anal ...

Transformation kernel estimation of insurance claim cost distributions 45 Given a sampleX 1 ,...,Xnof independent and identicall ...

46 C. Bolanc ́e, M. Guill ́en, and J.P. Nielsen which should be as close as possible to aBeta( 3 , 3 ). We can obtain an exact v ...

Transformation kernel estimation of insurance claim cost distributions 47 And finally, the optimal bandwidth parameter based on ...

48 C. Bolanc ́e, M. Guill ́en, and J.P. Nielsen 4 Simulation study This section presents a comparison of our inverse beta transf ...

Transformation kernel estimation of insurance claim cost distributions 49 Ta b le 2 .Estimated error measures (L 1 ,L 2 andWISE) ...

50 C. Bolanc ́e, M. Guill ́en, and J.P. Nielsen is shown by the other error measures,L 1 andL 2 ,whichforN=1000, are about 15 % ...

Transformation kernel estimation of insurance claim cost distributions 51 Acknowledgement.The Spanish Ministry of Education and ...

...

What do distortion risk measures tell us on excess of loss reinsurance with reinstatements? Antonella Campana and Paola Ferretti ...

54 A. Campana and P. Ferretti in the proposal of Walhin and Paris of the PH-transform risk measure strengthens our interest in t ...

Distortion risk measures,XLreinsurance and reinstatements 55 We consider an insurance portfolio:Nis the number of claims that oc ...

56 A. Campana and P. Ferretti 3 Initial premium, aggregate claims and distortion risk measures The total premium incomeδ(P)is a ...

Distortion risk measures,XLreinsurance and reinstatements 57 where the distortion functiongis defined as a non-decreasing functi ...

58 A. Campana and P. Ferretti Definition 1.Let g 1 and g 2 be distortion functions. The initial risk-adjusted premium P is the u ...

Distortion risk measures,XLreinsurance and reinstatements 59 the gradient vector∇f(c)is ∇f(c)= ( ∂f ∂cl (c) ) = ⎛ ⎜ ⎝ −AWg 1 (LX ...

60 A. Campana and P. Ferretti where the premium for theith reinstatement (4) is a two-point random variable dis- tributed asciPB ...

Distortion risk measures,XLreinsurance and reinstatements 61 Dhaene, J., Vanduffel, S., Tang, Q.H., Goovaerts, M.J., Kaas, R., ...

...

Some classes of multivariate risk measures Marta Cardin and Elisa Pagani Abstract.In actuarial literature the properties of risk ...