In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. Applying the Lamperti transformation we obtain a unique decomposition of a symmetric stable self-similar process into three independent parts: mixed...

In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal...

It is common practice in most insurance lines for the coverage to be restricted by a deductible. In the paper we investigate the influence of deductibles on pure risk premiums. We derive simple but practical formulae for premiums under franchise, fix amount, proportional, limited proportional...

In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss alpha-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a...

CONTENTS: 1.Introduction; 2.Financial market; 3.Securities; 4.Forwards, futures and options; 5.Financial mathematics of discrete models; 6.Financial mathematics of continuous models; 7.Term structure modeling; 8.Construction and pricing of exotic derivatives; 9.Statistics of financial markets;...

CONTENTS: Preliminary remarks; Brownian motion, poisson process, alpha-stable Levy motion; Computer simulation of alpha-stable random variables; Stochastic integration; Spectral representations of stationary processes; Computer approximations of continuous time processes; Examples of...

CONTENTS: 1.Introduction; 2.Financial market; 3.Electricity market; 4.Power exchange; 5.Forwards, futures and options; 6.Risk management; 7.Software (SPIS TRESCI: 1.Wprowadzenie; 2.Rynek finansowy; 3.Rynek energii elektrycznej; 4.Gielda energii elektrycznej; 5.Kontrakty terminowe; 6.Zarzadzanie...

The purpose of this paper is to show that using the toolkit of interest rate theory, already well known in financial engineering as the HJM model [D. Heath, R. Jarrow, A. Morton, Econometrica 60, 77 (1992)], it is possible to derive explicite option pricing formula and calibrate the theoretical...