An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Dynamic asset (and liability) management under market and credit risk

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a mul- tistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present a index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate our approach. In this way we are able to demonstrate the feasibility and flexibility of the chosen framework

A multiperiod multiobjective portfolio selection model with fuzzy random returns for large scale securities data

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordIt is agreed that portfolio selection models are of great importance for the financial market. In this article, a constrained multiperiod multiobjective portfolio model is established. This model introduces several constraints to reflect the trading restrictions and quantifies future security returns by fuzzy random variables to capture fuzzy and random uncertainties in the financial market. Meanwhile, it considers terminal wealth, conditional value at risk (CVaR), and skewness as tricriteria for decision making. Obviously, the proposed model is computationally challenging. This situation gets worse when investors are interested in a larger financial market since the data they need to analyze may constitute typical big data. Whereafter, a novel intelligent hybrid algorithm is devised to solve the presented model. In this algorithm, the uncertain objectives of the model are approximated by a simulated annealing resilient back propagation (SARPROP) neural network which is trained on the data provided by fuzzy random simulation. An improved imperialist competitive algorithm, named IFMOICA, is designed to search the solution space. The intelligent hybrid algorithm is compared with the one obtained by combining NSGA-II, SARPROP neural network, and fuzzy random simulation. The results demonstrate that the proposed algorithm significantly outperforms the compared one not only in the running time but also in the quality of obtained Pareto frontier. To improve the computational efficiency and handle the large scale securities data, the algorithm is parallelized using MPI. The conducted experiments illustrate that the parallel algorithm is scalable and can solve the model with the size of securities more than 400 in an acceptable time

New approaches to Risk Management and Scenario Approximation in Financial Optimization

The first part of the thesis addresses the problem of risk management in financial optimization modeling. Motivation for constructing a new concept of risk measurement is given through the history of development: utility theory, risk/return tradeoff, and coherent risk measures. The process of describing investor\u27s preferences is presented through the proposed collection of Rational Level Sets (RLS). Based on RLS, a new concept termed Rational Risk Measures (RRM) for nancial optimization models is defined. The advantages of RRM over coherent risk measures are discussed. Approximation of a given set of scenarios using tail information is addressed in the second part of the thesis. Motivation for the scenario approximation problem, as a way of reducing computation time and preserving solution accuracy, is given through examples of financial optimization and asset allocation models. Using the basic ideas of Conditional Value at Risk (CVaR), this thesis develops a new methodology for scenario approximation for stochastic portfolio optimization. First, the concepts termed Scenarios-at-Risk (SaR) and Scenarios-at-Gain (SaG) are proposed as for the purpose of partitioning the underlying multivariate domain for a xed investment portfolio and a fixed probability level of CVaR. Then, under a given set of CVaR values, a twostage method is developed for determining a smaller, and discrete, set of scenarios over which CVaR risk control is satisfied for all portfolios of interest. Convergence of the method is shown and numerical results are presented to validate the proposed technique

Portfolio construction by using different risk models : a comparison among diverse economic scenarios

We aim to construct portfolios by employing different risk models and compare their performance in order to understand their appropriateness for effective portfolio management for investors. Mean variance (MV), semi variance (SV), mean absolute deviation (MaD) and conditional value at risk (CVaR) are considered as risk measures. The price data were extracted from the Pakistan stock exchange, Bombay stock exchange and Dhaka stock exchange under diverse economic conditions such as crisis, recovery and growth. We take the average of GDP of the selected period of each country as a cut-off point to make three economic scenarios. We use 40 stocks from the Pakistan stock exchange, 92 stocks from the Bombay stock exchange and 30 stocks from the Dhaka stock exchange. We compute optimal weights using global minimum variance portfolio (GMVP) for all stocks to construct optimal portfolios and analyze the data by using MV, SV, MaD and CVaR models for each subperiod. We find that CVaR (95%) gives better results in each scenario for all three countries and performance of portfolios is inconsistent in different scenarios. © 2020 by the authors. Licensee MDPI, Basel, Switzerland

Aligning capital with risk

The interaction of capital and risk is of primary interest in the corporate governance of banks as it links operational profitability and strategic risk management. Senior executives understand that their organization's monitoring system strongly affects the behaviour of managers and employees. Typical instruments used by senior executives to focus on strategy are balanced scorecards with objectives for performance and risk management, including an according payroll process. A top-down capital-at-risk concept gives the executive board the desired control of the operative behaviour of all risk takers. It guarantees uniform compensations for business risks taken in any division or business area. The standard theory of cost-of-capital assumes standardized assets. Return distributions are equally normalized to a one-year risk horizon. It must be noted that risk measurement and management for any individual risk factor has a bottom-up design. The typical risk horizon for trading positions is 10 days, 1 month for treasury positions, 1 year for operational risks and even longer for credit risks. My contribution to the discussion is as follows: in the classical theory, one determines capital requirements and risk measurement using a top-down approach, without specifying market and regulation standards. In my thesis I show how to close the gap between bottom-up risk modelling and top-down capital alignment. I dedicate a separate paper to each risk factor and its application in risk capital management

Mathematical methods in modern risk measurement: a survey

In the last ten years we have been facing the development on new approaches in Risk Measurement. The Coherent, Expectation Bounded, Convex, Consistent, etc. Risk Measures have been introduced and deeply studied, but there are many open problems that will have to be addressed in forthcoming research. The present paper attempts to summarize the achieved findings and the “State of the Art”, as well as their relationships with other Mathematical Fields, with special focus on other usual topics of Mathematical Finance.En los últimos diez años hemos asistido al desarrollo de nuevos enfoques en Medición de Riesgos. Las Medidas de Riesgo Coherentes, Acotadas por la Media, Convexas, Consistentes, etc., han sido introducidas y profundamente estudiadas, aunque siguen abiertos numerosos problemas que tendrán que ser abordados en investigaciones futuras. El presente artículo sintetiza los logros alcanzados y “El Estado Actual de la Cuestión”, así como las relaciones con otros campos de la Matemática, con atención especial a los temas cl´asicos de la Matem´atica Financiera.This research was partially supported by “Welzia Management SGIIC SA”, “RD Sistemas SA”, “Comunidad Autonoma de Madrid ´ ” (Spain), Grant s-0505/tic/000230, and “MEyC” (Spain), Grant SEJ2006-15401-C04Publicad