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We propose and investigate a market model for power prices, including most basic features exhibited by previous models and taking into account self-exciting properties. The model proposed extends Hawkes-type models by introducing a two-fold integral representation property. A Random Field approach was already exploited by Barndorff-Nielsen et al., who adopted the Ambit Field framework for describing the power price dynamics. The novelty contained in our approach consists in combining the basic features of both Branching Processes and Random Fields in order to get a realistic and parsimonious model setting. We shall provide some closed-form evaluation formulae for forward contracts. We discuss the risk premium behavior, by pointing out that in the present framework, a very realistic description arises. We outline a possible methodology for parameters estimation. We illustrate by graphical representation the main achievements of this approach.

We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable Lévy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.

This paper concerns with the problem of determining an optimal control on the dividend and investment policy of a firm. We allow the company to make an investment by increasing its outstanding indebtedness, which would impact its capital structure and risk profile, thus resulting in higher interest rate debts. We formulate this problem as a mixed singular and switching control problem and use a viscosity solution approach combined with the smooth-fit property to get qualitative descriptions of the solution. We further enrich our studies with a complete resolution of the problem in the tworegime case.