Project Details
Projekt
Impulse Control Problems and Adaptive Numerical Solution of Quasi-Variational Inequalities in Markovian Factor Models
Subject Area
Mathematics
Term
from 2015 to 2019
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 265374484
Impulse control problems are ubiquitous when trading in financial markets. One striking example are portfolio optimization problems under transaction costs. Their mathematical description leads to quasi-variational inequalities, which typically do not admit analytical solutions. Current numerical methods, however, mostly do not incorporate adaptive techniques. Adaptive discretization is the key to an efficient and accurate determination of optimal trading strategies. In this project we shall develop adaptive methods and combine them with effective preconditioned solvers to obtain an efficient algorithm for the solution of quasi-variational inequalities. Integral terms, which occur in markets with jumps, will be included. Besides this, the current turbulence in financial markets, such as the credit crisis and the European financial crisis, puts the focus on increasing credit and counterparty risk. This asks for an extension of existing models. Markovian factor models are an appropriate tool to achieve a low-dimensional representation of complex dynamics on financial markets. We will formulate and analyze the ensuing problems as impulse control problems, for instance in portfolio optimization. Their solution will ask for those efficient and adaptive numerical methods for quasi-variational inequalities, which are developed as part of the project. Last but not least, the practical application requires the estimation of model parameters by means of historical data. This additional difficulty will be tackled by extending existing methodologies from incomplete information. The above-mentioned approaches will be extended in this direction. This is necessary to guarantee the practical applicability of the developed schemes.
DFG Programme
Research Grants
