TitleMulti-period scenario generation to support portfolio optimization
NameDeniz, Erhan (author), Luxhoj, James (chair), Boucher, Thomas (internal member), Coit, David (internal member), Papadakis, Yanni (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectIndustrial and Systems Engineering,
Portfolio management--Mathematical models
DescriptionStochastic Programming (SP) models are widely used for real life problems involving uncertainty. The random nature of problem parameters is modeled via discrete scenarios, which makes the scenario generation process very critical to the success of the overall approach. In this study we consider a portfolio management problem and propose two scenario generation algorithms and a SP model to support investment decisions. The main objective of the scenario generation algorithms is to infer representative probability values to be assigned to the scenario realizations sampled from historical data.
The first algorithm assigns the probabilities by using similarity scores, assigning higher probabilities to the scenarios with data paths that are relatively similar to historical paths, where similarity scores are computed by means of distance measures. We first implement this approach using the weighted Euclidean distance (WED). We also propose a new distance measure to obtain similarity scores as an alternative to WED.
The second scenario generation algorithm is based on the combination of moment-matching technique and the Exponential Generalized Auto-Regressive Conditional Heteroskedasticity (EGARCH) model. Scenario probabilities are assigned such that the first four moments of the sampled returns are fit to target moments through a linear programming model, where the second target moments are set to be conditional on the past scenarios on the scenario tree using the EGARCH model. An additional set of constraints are proposed to increase robustness.
The generated scenarios become input to the SP model to restructure the existing portfolio such that the expected final wealth is maximized and the risk exposure is controlled through constraining Conditional Value-at-Risk at each decision epoch on the scenario tree. We finally propose a generic approach to reduce potential losses and implement it on a logistic regression framework.
NoteIncludes bibliographical references (p. 216-220)
Noteby Erhan Deniz
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work