Robust Portfolio Optimization with Derivative Insurance Guarantees

Robust portfolio optimization aims to maximize the worst-case portfolio return given that the asset returns are allowed to vary within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns materialize far outside of the uncertainty set. We propose a novel robust portfolio optimization model that provides additional strong performance guarantees for all possible realizations of the asset returns. This insurance is provided via optimally chosen derivatives on the assets in the portfolio. The resulting model constitutes a convex second- order cone program, which is amenable to efficient numerical solution. We evaluate the model using simulated and empirical backtests and conclude that it can out- perform standard robust portfolio optimization as well as classical mean-variance optimization.robust optimization, portfolio optimization, portfolio insurance, second order cone programming

Optimization of vibratory energy harvesters with stochastic parametric uncertainty: a new perspective

Vibration energy harvesting has been shown as a promising power source for many small-scale applications mainly because of the considerable reduction in the energy consumption of the electronics and scalability issues of the conventional batteries. However, energy harvesters may not be as robust as the conventional batteries and their performance could drastically deteriorate in the presence of uncertainty in their parameters. Hence, study of uncertainty propagation and optimization under uncertainty is essential for proper and robust performance of harvesters in practice. While all studies have focused on expectation optimization, we propose a new and more practical optimization perspective; optimization for the worst-case (minimum) power. We formulate the problem in a generic fashion and as a simple example apply it to a linear piezoelectric energy harvester. We study the effect of parametric uncertainty in its natural frequency, load resistance, and electromechanical coupling coefficient on its worst-case power and then optimize for it under different confidence levels. The results show that there is a significant improvement in the worst-case power of thus designed harvester compared to that of a naively-optimized (deterministically-optimized) harvester. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Learning from data with uncertainty: Robust multiclass kernel-based classifiers and regressors.

Motivated by the presence of uncertainty in real data, in this research we investigate a robust optimization approach applied to multiclass support vector machines (SVMs) and support vector regression. Two new kernel based-methods are developed to address data with uncertainty where each data point is inside a sphere of uncertainty. For classification problems, the models are called robust SVM (R-SVM) and robust feasibility approach (R-FA) respectively as extensions of SVM approach. The two models are compared in terms of robustness and generalization error. For comparison purposes, the robust minimax probability machine (MPM) is applied and compared with the above methods. From the empirical results, we conclude that the R-SVM performs better than robust MPM. For regression problems, the models are called robust support vector regression (R-SVR) and robust feasibility approach for regression (R-FAR.). The proposed robust methods can improve the mean square error (MSE) in regression problems

A note on robust 0-1 optimization with uncertain cost coefficients

Based on the recent approach of Bertsimas and Sim (2004, 2003) to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. We exploit the binary nature of the optimization problem in proving our results. A discussion on the cost of ignoring uncertainty is also included. © 2004 Springer-Verlag Berlin/Heidelberg