A successive SDP-NSDP approach to a robust optimization problem in finance

Authors:
F. Leibfritz;J. H. Maruhn
Affiliations:
FB-IV Department of Mathematics, University of Trier, Trier, Germany 54286;Financial Engineering Equities and Hybrids, University of Trier and UniCredit Markets & Investment Banking, HypoVereinsbank, Munich, Germany 81925
Venue:
Computational Optimization and Applications
Year:
2009

Citing 11
Cited 0

Matrix analysis

Matrix analysis
Practical methods of optimization; (2nd ed.)

Practical methods of optimization; (2nd ed.)
Semidefinite programming

SIAM Review
Robust Control via Sequential Semidefinite Programming

SIAM Journal on Control and Optimization
An LMI-Based Algorithm for Designing Suboptimal Static $\cal H_2/\cal H_\infty$ Output Feedback Controllers

SIAM Journal on Control and Optimization
An Interior Point Constrained Trust Region Method for a Special Class of Nonlinear Semidefinite Programming Problems

SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization

SIAM Journal on Optimization
Robust portfolio selection problems

Mathematics of Operations Research
Optimization and Pseudospectra, with Applications to Robust Stability

SIAM Journal on Matrix Analysis and Applications
Successive Linearization Methods for Nonlinear Semidefinite Programs

Computational Optimization and Applications
Robust solutions of uncertain linear programs

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

The robustification of trading strategies is of particular interest in financial market applications. In this paper we robustify a portfolio strategy recently introduced in the literature against model errors in the sense of a worst case design. As it turns out, the resulting optimization problem can be solved by a sequence of linear and nonlinear semidefinite programs (SDP/NSDP), where the nonlinearity is introduced by the parameters of a parabolic differential equation. The nonlinear semidefinite program naturally arises in the computation of the worst case constraint violation which is equivalent to an eigenvalue minimization problem. Further we prove convergence for the iterates generated by the sequential SDP-NSDP approach.