# Multi-ITN STRIKE - Novel Methods in Computational Finance

## Contents

## Introduction

STRIKE is a Marie Curie International Training Network (ITN, 01/2013 - 12/2016) Acknowledgement: Short reference for contract: PITN-GA-2012-304617 STRIKE. |
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## Project Background

In recent years the computational complexity of mathematical models employed in financial mathematics
has witnessed a tremendous growth. **Advanced numerical techniques** are imperative for the
most present-day applications in financial industry.

The motivation for this training network is the need for a network of highly educated European scientists
in the field of financial mathematics and computational science, so as to exchange and discuss
current insights and ideas, and to lay groundwork for future collaborations.

Besides a series of internationally recognized researchers from academics, leading quantitative analysts
from the financial industry also participate in this network. The challenge lies in the necessity of
**combining transferable techniques and skills** such as mathematical analysis, sophisticated numerical
methods and stochastic simulation methods with deep qualitative and quantitative understanding
of mathematical models arising from financial markets.

The main training objective is to prepare, at the highest possible level, young researchers with a broad
scope of scientific knowledge and to teach **transferable skills, like social awareness** which is very
important in view of the recent financial crises.

The current topic in this network is that the **financial crisis in the European countries**
is a **contagion and herding effect** and is clearly outside of the domain of validity of Black-Scholes and Merton’s
theory, since the **market is not Gaussian and it is not frictionless and complete**.

In this research training network our aim is to **deeper understand complex (mostly nonlinear)
financial models and to develop effective and robust numerical schemes for solving linear and
nonlinear problems** arising from the mathematical theory of pricing financial derivatives and related
financial products. This aim will be accomplished by means of financial modelling, mathematical
analysis and numerical simulations, optimal control techniques and validation of models.

## Public Reports

An **Online** general overview is given in

- Z. Bucková, J.P. Campos Moreira da Silva, M. Ehrhardt, M. Günther, E.J.W. ter Maten:
*STRIKE - Novel Methods in Computational Finance - A European mathematical research training network*. IMACM-Report 2014-01, Bergische Universität Wuppertal, 2014.**Online:**ECMI Newsletter 55, pp. 9-12, 2014 (ECMI=European Consortium for Mathematics in Industry).

Each STRIKE Fellow did publish with his/her supervisor(s) an **"A4 report/flyer"** in the **Online** ECMI Newsletter 56, 2014, pp. 71-91:

- Z. Bučková (ESR1), M. Ehrhardt:
*Splitting Methods on Special Meshes*,**Online**ECMI Newsletter 56, 2014, pp. 71-72.

- J.P. Silva (ESR2), E.J.W. ter Maten, M. Günther:
*POD in Option Pricing: Basket Options and Heston Model*,**Online**ECMI Newsletter 56, 2014, pp. 73-74.

- P. Pólvora (ESR3), D. Ševčovič, M. Guerra:
*Pricing Derivatives in Markets with Transaction Costs*,**Online**ECMI Newsletter 56, 2014, pp. 74-75.

- V. Egorova (ESR4), L. Jódar Sánchez, R. Company Rossi:
*FDMs and Transformation Methods for nonlinear BS equations*,**Online**ECMI Newsletter 56, 2014, pp. 76-77.

- W. Mudzimbabwe (ESR5), L. Vulkov:
*Fitted Operator Methods and Special Meshes in Computational Finance*,**Online**ECMI Newsletter 56, 2014, pp. 77-78.

- N. Cantarutti (ESR6), M. do Rosário Grossinho, M. Guerra, J. Guerra:
*Option Pricing in Exponential Lévy Models with Transaction Costs*,**Online**ECMI Newsletter 56, 2014, pp. 79-80.

- I.P. Yamshchikov (ESR7), L.A. Bordag:
*Portfolio Optimization for an Illiquidity Asset with a Random Liquidation Time*,**Online**ECMI Newsletter 56, 2014, pp. 80-81.

- L. Trussardi (ESR8), A. Jüngel:
*Herding Behaviour in Financial Markets*,**Online**ECMI Newsletter 56, 2014, pp. 82-83.

- A. Leitao (ESR9), C.W. Oosterlee:
*GPU Acceleration of the Stochastic Grid Bundling Method*,**Online**ECMI Newsletter 56, 2014, pp. 84-85.

- S.-H. Tan (ESR10), C.-H. Lai:
*Newton-like Method for Nonlinear Option Pricing*,**Online**ECMI Newsletter 56, 2014, pp. 85-86.

- B. Gaviraghi (ESR11), A. Borzì:
*An Operator Splitting Method for Solving a Class of Partial-Integro Fokker-Planck Equations*,**Online**ECMI Newsletter 56, 2014, pp. 87-88.

- R. Valkov (ESR12), K. in ’t Hout:
*ADI time-stepping for the uncertain correlation Black–Scholes PDE*,**Online**ECMI Newsletter 56, 2014, pp. 88-89.

- M. Pou Bueno (ER4), C.W. Oosterlee:
*Pricing and Hedging by Backward Stochastic Differential Equations*,**Online**ECMI Newsletter 56, 2014, pp. 90-91.

## Work Packages - Project Structure

- WP 1: Modelling and Analysis
- WP 2: Numerical Methods for Nonlinear Models
- WP 3: Scientific Computing
- WP 4: Validation and Calibration
- WP 5: Complementary Skills Training
- WP 6: Dissemination and Exploitation
- WP 7: Management