Research interests (in
Applied probability, Computational finance, MCMC, Queueing
theory, Rare-event analysis, Simulation methodology, and Risk theory.
You can see publications here
Some Research Projects
The next are very brief and informal descriptions which
intended for students who are interested in stochastic systems. If you wish to
know more about these projects send me an email to set up a time to meeting in
person. These descriptions are not given in any particular order.
- Rare event analysis: This project
involves development of methodology for efficient simulation of
probabilities that are small such as the probabilities of bankruptcy. The
outcomes of these projects can be applied to problems involving finance,
insurance and queueing theory.
- Perfect Sampling: Traditionally, Perfect
Sampling or Exact Simulation algorithms related to the class of procedures
that allow to obtain samples in finite time from steady-state
distributions. These days, Exact Simulation also encompasses simulation
from fully continuous processes (such as SDEs). Our goal is to develop efficient
perfect sampling algorithms for a large class of stochastic processes.
- Limit theorems and asymptotic analysis:
In performance analysis of stochastic systems researchers use Brownian
motion and/or other types of stochastic processes as tractable
approximations to quantities of interest. We develop large deviations
results and corrections to these approximations (such as
performance analysis: Our goal is to quantify the impact of model
misspecification in performance analysis and control of stochastic system.
This is a very active research area and we put special emphasis on rare
insurance and pension fund systems: This represents a comprehensive
analysis of life insurance and pension fund systems from both the financial
and the risk theory perspectives. The goal is to develop a methodology
that allows to study and design these types of systems, using the theory
of many server queues, by considering both the market and insurance risks
at the same time.
models: The aim of this project is to develop theory applicable to
current risk models, for example, risk theory with investments and also
develop new models in a systemic / multidimensional setting. We try to
combine optimization theory and rare event simulation and we include
applications in areas such as insurance, distribution networks, and power