__Research interests (in
alphabetical order)__

Applied probability, Computational finance, MCMC, Queueing theory, Rare-event analysis, Simulation methodology, and Risk theory.

**You can see publications and preprints here**

__Some Research Projects__

The next are very brief and informal descriptions which
intended for students who are interested in stochastic systems. No references
are given below but you can google the key words to
find the references. If you wish to know more about these projects send me an
email to set up a time to meeting in person! Please, note that these
descriptions **are not given in any particular order** (also, not all the
current projects are listed here).

**Corrected Heavy-traffic Approximations**: In performance analysis of engineering systems researchers use Brownian motion and/or other types of stochastic processes as tractable approximations to quantities of interest. The approximations are often developed in a regime that is close to the critical capacity of the system (in the queueing context, this corresponds to heavily loading the system, therefore the name heavy-traffic). This project is about developing*corrections*to these approximations. As a particular case you can consider corrections to the standard CLT for iid rv’s, although these are very well understood and are called Edgeworth expansions.

**Perfect Sampling**: Perfect Sampling or Exact Simulation algorithms are the class of procedures that allow to obtain samples in finite time from the stationary distribution of a given Markov chain. The impact of these algorithms could, in principle, be enormous in MCMC (Markov Chain Monte Carlo) applications. However, these procedures are still not common in MCMC due to a number of issues. The goal of this project is to address these issues and make (as much as possible) perfect samplers a more routine tool in MCMC.

**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 design these types of systems by considering both the market and insurance risks at the same time.

**Credit risk models:**The aim of this project is two fold: a) study the properties of a class of models that extend classical models in the literature and that can be used for pricing and risk assessment of complex securities and b) to test the statistical validity of the model against actual data.

**Rare event analysis:**This project involves development of methodology for efficient simulation of probabilities that are small such as the probabilities of bankruptcy. The outcome of this project can be applied to problems involving finance, insurance and queueing theory.

**Risk theory with investments:**In this project we are interested in developing a flexible, yet powerful, framework to assess the risk of bankruptcy of an insurance company evolving in a stochastic economic environment.

**Large Call Centers in Heavy-traffic:**From a technical standpoint the purpose of this project is to understand the fine structure of large call centers in heavy-traffic. This problem presents many challenges and is great interest for the OR community. The outcome of this project would provide powerful tools to estimate important performance measures in the analysis of call centers.