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...

Using dynamic programming techniques the optimal exercise time for American warrants on WIG20 futures is found.

Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of...

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another...

The ruin probability in finite time can only be calculated analytically for a few special cases of the claim amount distribution. The most classic example is discussed in Section 1.2. The value can always be computed directly using Monte Carlo simulations, however, this is usually a...

A simple Ising spin model which can describe a mechanism of making a decision in a closed community is proposed. It is shown via standard Monte Carlo simulations that very simple rules lead to rather complicated dynamics and to a power law in the decision time distribution. It is found that a...

In 2000 we proposed a sociophysics model of opinion formation, which was based on trade union maxim "United we Stand, Divided we Fall" (USDF) and latter due to Dietrich Stauffer became known as the Sznajd model (SM). The main difference between SM compared to voter or Ising-type models is that...

Using an agent-based modeling approach we show how personal attributes, like conformity or indifference, impact opinions of individual electricity consumers regarding innovative dynamic tariff programs. We also examine the influence of advertising, discomfort of usage and the expectations of...

We modify a two-dimensional variant of a two-state non-linear voter model and apply it to understand how new ideas, products or behaviors spread throughout the society in time. In particular, we want to find answers to two important questions in the field of diffusion of innovation: Why does the...