Probabilistic Portfolio Modeling in Python

Master's thesis in Petroleum engineeringThe portfolio selection problem has been known for centuries. However, Markowitz (1952) was the first to introduce a robust framework for optimized portfolios on financial markets. Later this approach was applied in the petroleum industry to increase the corporate performance of oil and gas companies and to manage associated risks (Hightower et al. (1991)). Nevertheless, despite the lack of uncertainty optimization, simple portfolio selection techniques such as the Rank and Cut method remains popular in the industry (Wood (2016)). In this thesis, the advantages and disadvantages of this approach were briefly mentioned. Besides Markowitz Portfolio Theory and the Rank and Cut Method, a number of new portfolio selection methods were developed that not only improve the performance and minimize the risks but also can be used as processes and tools to deliver shareholder value or to achieve strategic corporate goals. One such approach is the use of multi-objective time series portfolio optimization, where the corporate goals are defined as constraints, the level of constraint accomplishment is quantified in terms of probability of exceeding the constraint and net present value is set as the main objective. This method was used to select an optimal portfolio from the pool of petroleum projects. One of the main contributions of this work is to provide a tool and process that can be used by management teams to evaluate different portfolios quickly using multiple time-dependent corporate constraints. The tool can be used to evaluate the impact on the portfolio of changing constraints or weighting the constraints differently. The ability to do this interactively is essential as it allows the management team to evaluate and address the key elements of their portfolio decision problem. A crucial part of the portfolio optimization problem is the choice of optimization algorithms. Several algorithms that facilitate the petroleum industry’s needs of portfolio optimization were studied, and a brief overview of them was presented. We also included a discussion of the choice of programming language for portfolio models. Although we built the project model in R, we ended up using Python as it provided significant computational speed improvements over R. We also argued why Excel, although very popular, is far from an optimal tool for portfolio modeling

Multi-Objective Stochastic Optimization Programs for a non-Life Insurance Company under Solvency Constraints

In the paper, we introduce a multi-objective scenario-based optimization approach for chance-constrained portfolio selection problems. More specifically, a modified version of the normal constraint method is implemented with a global solver in order to generate a dotted approximation of the Pareto frontier for bi- and tri-objective programming problems. Numerical experiments are carried out on a set of portfolios to be optimized for an EU-based non-life insurance company. Both performance indicators and risk measures are managed as objectives. Results show that this procedure is effective and readily applicable to achieve suitable risk-reward tradeoff analysis

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

A note on evolutionary stochastic portfolio optimization and probabilistic constraints

In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are ideally suited for an integration of various types of probabilistic constraints. We show an approach on how to integrate these constraints. Numerical results using recent financial data substantiate the applicability of the presented approach

Proteus: A Hierarchical Portfolio of Solvers and Transformations

In recent years, portfolio approaches to solving SAT problems and CSPs have become increasingly common. There are also a number of different encodings for representing CSPs as SAT instances. In this paper, we leverage advances in both SAT and CSP solving to present a novel hierarchical portfolio-based approach to CSP solving, which we call Proteus, that does not rely purely on CSP solvers. Instead, it may decide that it is best to encode a CSP problem instance into SAT, selecting an appropriate encoding and a corresponding SAT solver. Our experimental evaluation used an instance of Proteus that involved four CSP solvers, three SAT encodings, and six SAT solvers, evaluated on the most challenging problem instances from the CSP solver competitions, involving global and intensional constraints. We show that significant performance improvements can be achieved by Proteus obtained by exploiting alternative view-points and solvers for combinatorial problem-solving.Comment: 11th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. The final publication is available at link.springer.co

An Enhanced Features Extractor for a Portfolio of Constraint Solvers

Recent research has shown that a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. The solver selection is usually done by means of (un)supervised learning techniques which exploit features extracted from the problem specification. In this paper we present an useful and flexible framework that is able to extract an extensive set of features from a Constraint (Satisfaction/Optimization) Problem defined in possibly different modeling languages: MiniZinc, FlatZinc or XCSP. We also report some empirical results showing that the performances that can be obtained using these features are effective and competitive with state of the art CSP portfolio techniques