Research interests (in alphabetical order)

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.

 

  1. 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.

 

  1. 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.

 

  1. 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 Edgeworth-type expansions).

 

  1. Robust 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 event analysis.

 

  1. Life 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.

 

  1. Risk 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 systems.