Blog de la Biblioteca de Matemàtiques i Informàtica

SIMBa: Stochastic Differential Equations

Dilluns, 7 d’abril, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: David Ruiz
Universitat: Universitat d’Oslo (Department of Mathematics)

Data: dilluns, 7 d’abril de 2014
Hora: 17:45, cafè; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Stochastic Differential Equations.
Resum: In this talk we want to explain what a stochastic differential equation (SDE) is. As an idea, we will recall what a (deterministic) ordinary differential equation (ODE) is and then we will add some “noise” to it. Such equations are widely used to study and model phenomena in nature such as for instance: the “random” movement of a particle in a fluid due to collisions with the molecules of the fluid, variable uncertainty, macroeconomic dynamics, etc. The solution of an SDE is therefore a stochastic process, i.e. think of it as a function whose image is not a real number, but a random variable. It is a big area of research to study the solutions of SDE’s and the densities of such solutions. It is very difficult to say something about the densities.

An SDE looks typically like

$dx(t) = f(t,x(t))dt + "noise", t_0\leq t \leq a, x(t_0)=x_0\in \mathbb{R}$

where the initial condition $x(t_0)=x_0$ is typically taken as a deterministic point $x_0 \in \mathbb{R}$ that we have observed or might also be taken as $x(t_0) = Z$ where $Z$ is a random variable (e.g. normal distributed).

Finally, we will mention some properties of SDE’s, like… For example, you know that the solution when $f$ is Lipschitz exists and it is unique for ODE’s (Picard’s theorem). In the case of SDE’s even if $f$ is very “ugly” a unique solution also exists! Meaning that, the “noise” somehow regularizes $x(t)$.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

SIMBa: An approach to Mathematical Finance

Dimarts 21 de febrer se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona.

Speaker: David Ruiz
UniversitatUniversitetet i Oslo

Data: dimarts 21 de febrer de 2012
Hora: 17:15, cafè i galetes; 17:30, inici

Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: An approach to Mathematical Finance
Resum: Mathematics has become a very important tool for the good management of the economy of a financial or insurance company and the correct way of pricing financial instruments is also of relevance, as well as the good way to manage with the risk of a strategy when investing in a financial market.
In this talk we will have a preliminary introduction on financial concepts such as, financial market, self-financing portfolio, financial contract, the concept of risk, and more. We will also introduce the Black-Scholes-Merton model.

Then, we will talk about pricing theory and introduce a way to price financial contracts following what is known as the arbitrage-free principle. We will explain the concept of arbitrage and show some formulas to price financial options. We will also try to introduce the change of numéraire technique.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a simba(at)imub(dot)ub(dot)es