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;...

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...

In this paper we apply a new approach to build bidding strategies for power suppliers on electricity market and assume that each supplier’s bid is a linear function. Moreover each supplier tends to maximise his profit and minimize his risk, which are dependent on the generation output,...

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

The main purpose of the paper is to present, how derivatives valuing methodology, known from financial and commodities markets, can be applied to the electricity market. We compare an application of three recent models. We start with the convenience yield approach, then we analyse the...