We give a short introduction to the stochastic calculus for Itô-Lévy processes and review briefly the two main methods of optimal control of systems described by such processes: (i) Dynamic programming and the ...

Due to the non-storability of electricity and the resulting lack of arbitrage-based arguments to price electricity forward contracts, a significant time-varying risk premium is exhibited. Using EEX data during the introduction ...

The aim of this paper is to introduce a new numerical algorithm for solving the continuous time nonlinear filtering problem. In particular, we present a particle filter that combines the Kusuoka–Lyons–Victoir (KLV) cubature ...

We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a ...

In this paper we propose a new modelling framework for electricity futures markets based on so-called ambit fields. The new model can capture many of the stylised facts observed in electricity futures and is highly ...

By a memory mean-field process we mean the solution X(\cdot ) of a stochastic mean-field equation involving not just the current state X(t) and its law \mathcal {L}(X(t)) at time t, but also the state values X(s) and its ...

We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward–backward stochastic differential equations. We prove general stochastic ...

We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial ...

We study stochastic differential games of jump diffusions driven by Brownian motions and compensated Poisson random measures, where one of the players can choose the stochastic control and the other player can decide when ...

This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by Itô-Lévy processes, but it also contains some new results on the underlying stochastic ...