Manuel Morales, Ph.D.

Associate Professor

## Publications

On the Time-value of Ruin for a Markov-additive Risk Process.Computing the finite-time expected discounted penalty function for a family of Levy risk processes.

On the Price of Risk of the Underlying Markov Chain in a Regime-switching Exponential Levy Model.

Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator.

## Conference Presentations

35th Conference on Stochastic Processes and their Applications. Oaxaca, Mexico (June 19-25, 2011)15th International Congress on Insurance: Mathematics and Economics. University of Trieste, Trieste, Italy (June 14-17, 2011)

5th Brazilian Conference on Statistical Modelling in Insurance and Finance Maresias, Brazil (April 10-15, 2011)

## Projects

MITACS Finsurance ProjectLévy Risk Processes

Econophysics

## My Students

Maciej AugustyniakZyed Ben Salah

Raymond Elmahdaoui

Ionica Groparu

Romuald Momeya

Hassan Omidi

## Research at DMS

Insurance and FinanceMITACS Seminar in Montreal

## Research Abroad

List of Univeristies

## Journals

Insurance: Mathematics and EconomicsNorth American Actuarial Journal

Scandinavian Actuarial Journal

ASTIN Buletin

Finance and Stochastics

Mathematical Finance

Mathematical and Financial Economics

## Links

ISM Research Group in Finance and InsuranceCentre de Recherches Mathématiques

NSERC

FQRNT

MITACS

## Research

My main research interest is in the field of Ruin Theory, particularly in Lévy Risk Processes and their associated expected discounted penalty functions. I am currently working on generalizations using Lévy processes as models for the aggregate claims. These applications are related to the first-passage time problem of a Lévy process.I am also interested in Option Pricing, particularly in jump models that use Lévy processes with a jump component to describe stock price processes instead of the geometric Brownian Motion. Applications of Generalized Hyperbolic Lévy motion and other pure jump processes in insurance and in finance are also among my interests.

More recently, I have have started to turn my attention to other interesting subjects such as:

Convex and Distortion Risk Measures

Lévy Regime Switching Models

Position Dependent Random Maps in Finance

## Projects

My current research is mainly carried out as part of the following on-going research projects.**MITACS Finsurance Project**

Recently, we observe the appearance in the market of new products that blend risk features from both finance and insurance. This has created a new hybrid class of products known as "finsurance" products. The valuation, hedging and risk analysis of such hybrid products demand novel and innovative tools combining expertise in finance, actuarial science, probability theory, differential equations and numerical methods. This project is focused on developing these analytical tools, and applying them to the problems confronting the insurance and finance sector generally.

**Lévy Risk Processes Project**

Risk Theory traditionally studies ruin related quantities for risk reserves models. This is linked to the first-passage time problem which is well-understood for different classes of processes, in particular for Lévy processes. This project focuses on studying traditionlly risk theory models from a the perspective offered by these new results in fluctuation theory for stochastic processes. There are different aspects and/or variations of this problem that are of the object of our interest such as: identifying Lévy processes for which numerical computations can be carried out, studying ruin problems for regime switching models and non-homogeneous processes, generalizing existing results for a bivariate Lévy risk model with two sources of risk and finally developping ruin-based risk measures for insurance applications.

## Students

I currently supervise the following Ph.D. students. They are all involved in different aspects of the research projects described above.Hirbod Assa

Zyed Ben Salah

Ionica Groparu

Romuald Momeya

My research has been funded by: