Abstract
We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modelling the convergence of the buyer's and of the seller's prices to a unique price are proposed.

Abstract
The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We determine the analytic formula that describes the fine balance between Regulatory T cells and T cells at controlled and immune response equilibrium states. We demonstrate that cytokine dependent growth exhibits a quorum T cell population threshold that determines if immune responses develop on activation. We determine the analytic formulas of T cell proliferation thresholds that allow us to study the sensibility of the quorum growth thresholds controlling immune responses.

Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 secretion. The bystander proliferation to an immune response is modelled. We consider an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and Tregs than for the inactive. This asymmetry leads to a better understanding of the bystander proliferation. An exposure to a pathogen results in an increased proliferation rate of the bystander T cells. If the population of the bystander T cells becomes large enough, autoimmunity can arise, eventually after a long transient period.

Abstract
We introduce a resort pricing model, where different types of tourists choose between different resorts. We study the influence of the resort prices on the choices of the different types of tourists. We characterize the coherent strategies of the tourists that are Nash equilibria. We find the prices that lead to the bankruptcy of the resorts and, in particular, their dependence on the characteristics of the tourists.

Abstract
We use a new R&D investment function in a Cournot competition model inspired in the logistic equation. We present the full characterization of the associated gam; and study the short and long term economical effects derived from using this new R&D investment function. We observe the existence of four different Nash investment equilibria regions and fully characterize the boundaries of these regions.

Abstract
We introduce a renormalization scheme to study the asymptotic dynamical behaviour of a family of mechanical systems with non-isochronous potentials with an elliptic equilibrium. This renormalization scheme acts on a family of orbits of these mechanical systems, all of which are contained on neighbourhoods of the elliptic equilibrium, by rescaling space and shifting time in an appropriate way. We present some new results regarding the properties of this renormalization scheme, and examine the strong connection it has with the focal decomposition for the Euler-Lagrange equation of this family of mechanical systems.