A discrete time model of a financial market is considered. We focus on the study of a guaranteed profit of an investor which arises when the stock price jumps are bounded. The limit distribution of the profit as the model becomes closer to the classical model of the geometric Brownian motion is...

We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index'' n that quantifies the degree of endogeneity...

We study a combination of the refracted and reflected Levy processes. Given a spectrally negative Levy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a constant rate is subtracted from the increments of the...