Catálogo de publicaciones - libros

In this paper we study the jump-diffusion CIR process (shorted as JCIR), which is an extension of the classical CIR model. The jumps of the JCIR are introduced with the help of a pure-jump Lévy process . Under some suitable conditions on the Lévy measure of , we derive a lower bound for the transition densities of the JCIR process. We also find some sufficient conditions under which the function , , is a Forster-Lyapunov function for the JCIR process. This allows us to prove that the JCIR process is exponentially ergodic.

We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process () and a backward SDE (BSDE) in the unknowns . The driver of the BSDE at time may depend not just upon the unknown processes , but also on the predicted future value , defined by the conditional expectation . We give a sufficient and a necessary maximum principle for the optimal control of such systems, and then we apply these results to the following two problems: (i) Optimal portfolio in a financial market with an (ii) Optimal consumption rate from a cash flow modeled as a geometric Itô-Lévy SDE, with respect to .

This paper studies the impact of wind power production on electricity prices in the European energy market. We propose a new modelling framework based on so-called regime-switching Lévy semistationary processes to account for forward-looking information consisting of predicted wind power generation. We show that our new regime-switching model, where the regime switch depends on the so-called wind penetration index, can describe recent electricity price data well.

To price options on emission certificates reduced-form models have proved to be useful. We empirically analyse the performance of the model proposed in Carmona and Hinz [] and Hinz []. As we find evidence for a time-varying market price of risk, we extend the Carmona-Hinz framework by introducing a bivariate pricing model. We show that the extended model is able to extract information on the market price of risk and evaluate its impact on the EUA options.