## Financial Mathematics

The goal at PhiMAC, the Financial Mathematics Laboratory, is to develop analytical and computational tools to analyse, model and make decisions in financial markets. Research focuses on a wide range of problems that include asset pricing, credit risk and interest rate modelling. In each of these areas, we pursue theoretical results (such as generalizing the usual Brownian motion assumptions to cases where markets are driven by more general jump processes) and address the related numerical implementation and calibration issues. For example, research in optimal portfolio selection uses convex analysis to study theoretical existence of an optimal choice of asset allocation under general market uncertainty, as well as numerical methods such as Monte Carlo simulations to actually construct such portfolios for given market data.

## Information Box Group

### Anas Abdallah

Associate Professor and AFM Coordinator

**Research Area: **Actuarial and Financial Mathematics

**Research Profile: **Actuarial Science

My research area is in actuarial science, with focus on: dependence modeling, loss reserving, capital allocation and predictive modeling in non-life insurance and ratemaking/pricing.

The objective of my research is to propose hierarchical statistical approaches to model dependence within and between risks in non-life insurance in general, and in a loss reserving context in particular. One of the most critical problems in Property & Casualty (P&C) insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. However, most risks are related to each other in practice, and this correlation needs to be taken into account.

### Anas Abdallah

**Associate Professor and AFM Coordinator**

### Matheus Grasselli

Professor and Deputy Provost

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics, Mathematical Physics, Information Geometry *

My main research interests lie in the area of mathematical finance – the application of stochastic analysis and probability theory to the understanding and modelling of financial markets. Specific projects I am involved with include numerical and theoretical optimal portfolio selection and modelling of positive interest rates. I am also interested in classical and quantum information geometry. My work in this area ranges from the construction of infinite dimensional manifolds of probabilities to the applications of such geometric objects to models in fluid dynamics and quantum information.”

### Anastasis Kratsios

Assistant Professor

I develop and study universal deep learning models capable of leveraging geometric structures in mathematical finance and data science problems.

### David Lozinski

Associate Professor and MFM Program Director

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics *

My research interests concern the mathematical modelling and analysis of problems in the area of quantitative finance. Of particular interest to me are problems that arise in credit risk, including issues of correlation, counterparty exposure, and capital assessment and allocation.

### David Lozinski

**Associate Professor and MFM Program Director**

### Traian Pirvu

Associate Professor

**Research Area:** Financial Mathematics

**Research Profile:** My main research lie in the area of financial mathematics with a special emphasis on optimal investment and pricing in incomplete markets. My projects are on equilibrium pricing of non tradable risks, optimal portfolio selection with regulatory constraints and time consistent portfolio management.

### Anas Abdallah

Associate Professor and AFM Coordinator

**Research Area: **Actuarial and Financial Mathematics

**Research Profile: **Actuarial Science

My research area is in actuarial science, with focus on: dependence modeling, loss reserving, capital allocation and predictive modeling in non-life insurance and ratemaking/pricing.

The objective of my research is to propose hierarchical statistical approaches to model dependence within and between risks in non-life insurance in general, and in a loss reserving context in particular. One of the most critical problems in Property & Casualty (P&C) insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. However, most risks are related to each other in practice, and this correlation needs to be taken into account.

### Anas Abdallah

Associate Professor and AFM Coordinator

**Research Area: **Actuarial and Financial Mathematics

**Research Profile: **Actuarial Science

My research area is in actuarial science, with focus on: dependence modeling, loss reserving, capital allocation and predictive modeling in non-life insurance and ratemaking/pricing.

The objective of my research is to propose hierarchical statistical approaches to model dependence within and between risks in non-life insurance in general, and in a loss reserving context in particular. One of the most critical problems in Property & Casualty (P&C) insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. However, most risks are related to each other in practice, and this correlation needs to be taken into account.

### Matheus Grasselli

Professor and Deputy Provost

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics, Mathematical Physics, Information Geometry *

My main research interests lie in the area of mathematical finance – the application of stochastic analysis and probability theory to the understanding and modelling of financial markets. Specific projects I am involved with include numerical and theoretical optimal portfolio selection and modelling of positive interest rates. I am also interested in classical and quantum information geometry. My work in this area ranges from the construction of infinite dimensional manifolds of probabilities to the applications of such geometric objects to models in fluid dynamics and quantum information.”

### Matheus Grasselli

Professor and Deputy Provost

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics, Mathematical Physics, Information Geometry *

My main research interests lie in the area of mathematical finance – the application of stochastic analysis and probability theory to the understanding and modelling of financial markets. Specific projects I am involved with include numerical and theoretical optimal portfolio selection and modelling of positive interest rates. I am also interested in classical and quantum information geometry. My work in this area ranges from the construction of infinite dimensional manifolds of probabilities to the applications of such geometric objects to models in fluid dynamics and quantum information.”

### Anastasis Kratsios

Assistant Professor

I develop and study universal deep learning models capable of leveraging geometric structures in mathematical finance and data science problems.

### Anastasis Kratsios

Assistant Professor

I develop and study universal deep learning models capable of leveraging geometric structures in mathematical finance and data science problems.

### David Lozinski

Associate Professor and MFM Program Director

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics *

My research interests concern the mathematical modelling and analysis of problems in the area of quantitative finance. Of particular interest to me are problems that arise in credit risk, including issues of correlation, counterparty exposure, and capital assessment and allocation.

### David Lozinski

Associate Professor and MFM Program Director

**Research Area:** Financial Mathematics

**Research Profile:** *Financial Mathematics *

My research interests concern the mathematical modelling and analysis of problems in the area of quantitative finance. Of particular interest to me are problems that arise in credit risk, including issues of correlation, counterparty exposure, and capital assessment and allocation.

### Traian Pirvu

Associate Professor

**Research Area:** Financial Mathematics

**Research Profile:** My main research lie in the area of financial mathematics with a special emphasis on optimal investment and pricing in incomplete markets. My projects are on equilibrium pricing of non tradable risks, optimal portfolio selection with regulatory constraints and time consistent portfolio management.

### Traian Pirvu

Associate Professor

**Research Area:** Financial Mathematics

**Research Profile:** My main research lie in the area of financial mathematics with a special emphasis on optimal investment and pricing in incomplete markets. My projects are on equilibrium pricing of non tradable risks, optimal portfolio selection with regulatory constraints and time consistent portfolio management.