Ornstein-Uhlenbeck type processes with heavy distribution tails (Q2863587)

The role of the Brownian motion, the Ornstein-Uhlenbeck (OU) process and Lévy processes is well recognised in the area of financial stochastic modelling. The authors start with an OU process \(X_t\), \(t\geq 0\), where \(dX_t= -\alpha X_tdt+\tau dW_t\); \(\alpha,\tau> 0\) are constants. The goal is to consider new processes, \(Y_t= h(X_t)\), for suitable transforming functions \(h\). From the theoretical point of view this is an interesting problem, and some results are known. It is however more delicate to choose transformations \(h\) which in one or another way are appropriate in financial models, in particular to make the model well replicating real stock market data.NEWLINENEWLINE The authors achieve both new theoretical results for which proofs are provided and a demonstration of good choices of \(h\). There is a lot in this paper: probability, statistical inference for continuous time processes using discrete observation, and impressive graph illustrations. The paper is well written, well motivated and will attract the attention of the community of stochastic financial modellers.