Random Fixed Points, Limits and Systemic risk

Speaker : Kavitha Veeraruna
IIT Bombay
Date: 13/12/2017
Time: 2:00 pm - 3:00 pm
Location: Doctoral Training Center (EIT Digital)


Abstract: We consider vector fixed point (FP) equations in large
dimensional spaces involving random variables, and study their
realization-wise solutions. We have an underlying directed random
graph, that defines the connections between various components of the
FP equations. Existence of an edge between nodes i,j implies the i-th
FP equation depends on the j-th component. We consider a special case
where any component of the FP equation depends upon an appropriate
aggregate of that of the random “neighbor” components. We obtain
finite dimensional limit FP equations (in a much smaller dimensional
space), whose solutions approximate the solution of the random FP
equations for almost all realizations, in the asymptotic limit (number
of components increase). Our techniques are different from the
traditional mean-field methods, which deal with stochastic FP equations
in the space of distributions to describe the stationary distributions
of the systems. In contrast our focus is on realization-wise FP
solutions. We apply the results to study systemic risk in a large
financial heterogeneous network with many small institutions and one
big institution, and demonstrate some interesting phenomenon.
Biography: Kavitha Veeraruna completed my PhD with Indian Institute of
Science in 2007. I have done two postdocs, one at TIFR Bangalore and
then with Prof. Eitan Altman at INRIA. Currently I am working as an
Assistant Professor at IIT Bombay Mumbai.