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.

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely...

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...

In this paper, we demonstrate some properties of Alpha-stable (stable) random variables and processes. It turns out that with the use of suitable statistical estimation techniques, computer simulation procedures and numerical discretization methods it is possible to construct approximations of...

In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to alpha-stable Levy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic...

In this paper we investigate properties of R-GARCH processes with positive strictly stable innovations. We derive the unconditional distributions and analyze the dependence structure. This analysis is carried out by means of the measure of dependence - the codifference - which extends the...

The Conditionally Exponential Decay (CED) model is used to explain the scaling laws observed in financial data. This approach enables us to identify the distributions of currency exchange rate or economic indices returns (changes) corresponding to the empirical scaling laws. This is illustrated...

In this paper, motivated by [2], we derive necessary and sufficient conditions for bounded and periodically correlated solutions to the system of equations described by ARMA(1,q) model.