Computational tools for simulation with differential equations

SPEAKER: Luz Myriam Echeverry

Universidad  Sergio Arboleda

ABSTRACT

The purpose of this talk is to tell about the research project that is being developed using differential equations

DATE:  Wednesday, October 14 th, 2015

TIME:  6:00 pm

CLASSROOM: A601

Combinatorial Micro-Macro Dynamical Systems

SPEAKER: Sergio Villamarin

Universidad  Sergio Arboleda

ABSTRACT

The second law of thermodynamics states that the Bolztman entropy of an isolated system almost always increases. We explore the possibilities for the second law within a purely combinatorial context. We focus in the extreme cases: full application and maximal failure of the law by some of the results in [1].

[1]  Rafael Diaz, Sergio Villamarin, arXiv:1507.06703v1 [math.CO]

DATE:  Wednesday, September 9 th, 2015

TIME:  6:00 pm

CLASSROOM: A601

Portfolio optimization in jump models with nonlinear wealth dynamics.

SPEAKER: Rafael Serrano

Universidad del Rosario

ABSTRACT

We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics. This allows to take account of relaxed assumptions such as differential borrowing and lending interest rates and/or short positions with cash collateral and negative rebate rates. We give sufficient conditions for existence of optimal policies for agents with logarithmic and CRRA power utility. We find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain.

DATE:  Wednesday, August 26 th, 2015
TIME:  6:00 pm

CLASSROOM: A601