In the article we consider accumulated values of annuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arithmetic and geometric progression which are important basic varying annuities (see Kellison, 1991). They are...

We demonstrate that continuous-time FARIMA processes with α-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of α-stability and self-similarity are implemented for...

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...

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency...

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply...