Seminars

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in portfolio optimization problem.

This talk will give general audience a brief introduction to biography of Thomas Bayes, Bayes Theorem and Bayesian Inference. Detailed illustration using examples is provided with emphasis on data analysis.

Using change of time method, we derive a closed-form formula for the volatility swap in an adjusted version of the Heston model with stochastic volatility with delay. The numerical result is presented for underlying EURUSD on September 30th 2011. The novelty of the result is two-fold: application of change of time method to the delayed Heston model and calculation of the volatility swap for this model.

The term "systemic risk" refers to the contagion-induced threat to the financial system as a whole, due to the default of one (or more) of its constituent institutions.  The ultimate question for me is how mathematical models can help us understand systemic risk. In this talk I will explore some of the background concepts, then look at certain  "deliberately simplified models of systemic risk" to see what they may say about the problem.

In order to obtain theorems such as:  Every bounded  uncountable separable homogeneous universal metric space is oscillation stable, some quite interesting problems in discrete mathematics had to be addressed.  One of them is the following: Let C be a class of metric spaces and G an edge labelled graph.  Under which conditions on C and G can the labelling of G be extended to a labelling of the complete graph with vertices V(G), so that the metric space on V(G) with distance between two points the label on the edge connecting them, is an element of C.  I will give some indication how a very special case of this problem relates to the theorem above and how this special case can be resolved.