On Finding Maximum Cardinality Subset of Vectors with a Constraint on Normalized Squared Length of Vectors Sum

In this paper, we consider the problem of finding a maximum cardinality subset of vectors, given a constraint on the normalized squared length of vectors sum. This problem is closely related to Problem 1 from (Eremeev, Kel'manov, Pyatkin, 2016). The main difference consists in swapping the constraint with the optimization criterion. We prove that the problem is NP-hard even in terms of finding a feasible solution. An exact algorithm for solving this problem is proposed. The algorithm has a pseudo-polynomial time complexity in the special case of the problem, where the dimension of the space is bounded from above by a constant and the input data are integer. A computational experiment is carried out, where the proposed algorithm is compared to COINBONMIN solver, applied to a mixed integer quadratic programming formulation of the problem. The results of the experiment indicate superiority of the proposed algorithm when the dimension of Euclidean space is low, while the COINBONMIN has an advantage for larger dimensions.Comment: To appear in Proceedings of the 6th International Conference on Analysis of Images, Social Networks, and Texts (AIST'2017

Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we perform two approximations: stage-aggregation and linear decision rules (LDR). The LDR approach consists of restricting the set of decision rules to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.OR in energy, electricity portfolio management, stochastic programming, risk management, linear decision rules

Risk-Constrained Forward Trading Optimization by Stochastic Approximate Dynamic Programming

Since the mid-twentieth century, Dynamic Programming (DP) has proved to be a flexible and powerful approach to address optimal decisions problems. Nevertheless, a decisive drawback of the conventional DP is the need for exploring the whole state space in order to find the optimal solution. The immense amount of mathematical operations involved to solve real-scale problems, constrained the application of DP to small or highly simplified cases. Indeed, state space grows exponentially with the number of variables when considering multivariate optimization. The curse of dimensionality is a well-known limitation of conventional DP algorithms for tackling large-scale problems ubiquitous in real science and engineering applications. In the last decades, many new algorithms emerged in different branches of science to overcome the inherent limitations of conventional DP. Unlike conventional DP, these algorithms avoid enumerating and calculating every possible state of a system during the optimization process. Instead, they estimate relevant features of the state space. This approach circumvents the dimensionality limitations of the conventional DP while retaining many of its advantages. In this chapter, the application of advanced stochastic dynamic programming techniques to the optimization of the forward sell strategy of a power generator subjected to delivery risk is considered. The proposed approach allows rebalancing the portfolio during the period of analysis. In electricity markets, a power generator can sell in advance part or all its future energy production at a fixed price, hedging against the high price volatility of the spot market. The strategy of eliminating the price risk by selling in advance the entire production in the forward market to a fixed price is often thought as the minimum-risk trading policy. Nonetheless, it can be proven that this is not the case for most generators. The outages of the generation units and transmission lines, as well as unforeseen limitations in the primary energy supply expose generators to delivery risk [1]. Delivery risk considerably modifies the probability distribution of profits, shifting the optimal trading strategy toward a portfolio mixing forward contracts and power sold in the spot market. Because of the size of the probability state space and the limited computing capabilities, the problem of the optimal trading strategy has not a closed form solution and thus, its determination is matter of current study. The increase in computing power and recent developments in Operational Research has brought new insights into the solution of such problems. In the past decade and by virtue of the ever increasing computational power, many methods emerged in different scientific fields with several different names: Reinforced Learning, QLearning, Neuro-Dynamic Programming, etc. All these methods were later brought together in what is currently known as Approximated Dynamic Programming (ADP) [2],[3]. These algorithms resign the exhaustive enumeration and calculation of the space-state typically performed by conventional DP. Instead, they iteratively approximate a function of the space state through stochastic simulation and statistical regression techniques, circumventing the dimensionality problem of DP. Although ADP algorithms are being used in several other fields of science, the application to design optimal trading strategies in power markets has not been proposed so far. In this chapter, ADP techniques are exploited to optimize the selling strategy of a power generator trading in a frictional market with transaction costs. Three available products are considered: selling in the spot market, and/or get involved in quarterly and one-year forward contracts. The objective of the generator is to maximize the expected profit while limiting financial risk. Decisions can be made only at the beginning of each month. At each decision stage, the current trading position can be changed at a cost in order to rebalance the portfolio.Fil: Gil Pugliese, Miguel Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Energía Eléctrica. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; Argentina. Instituto F/elektrische Anlagen & Energiewirtschaft; AlemaniaFil: Olsina, Fernando Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Energía Eléctrica. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; Argentin

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Optimisation of electricity energy markets and assessment of CO2 trading on their structure : a stochastic analysis of the greek power sector

Power production was traditionally dominated by monopolies. After a long period of research and organisational advances in international level, electricity markets have been deregulated allowing customers to choose their provider and new producers to compete the former Public Power Companies. Vast changes have been made in the European legal framework but still, the experience gathered is not sufficient to derive safe conclusions regarding the efficiency and reliability of deregulation. Furthermore, emissions' trading progressively becomes a reality in many respects, compliance with Kyoto protocol's targets is a necessity, and stability of the national grid's operation is a constraint of vital importance. Consequently, the production of electricity should not rely solely in conventional energy sources neither in renewable ones but on a mixed structure. Finding this optimal mix is the primary objective of the study. A computational tool has been created, that simulates and optimises the future electricity generation structure based on existing as well as on emerging technologies. The results focus on the Greek Power Sector and indicate a gradual decreasing of anticipated CO2 emissions while the socioeconomic constraints and reliability requirements of the system are met. Policy interventions are pointed out based on the numerical results of the model. (C) 2010 Elsevier Ltd. All rights reserved

Dynamic Programming and Bayesian Inference

Dynamic programming and Bayesian inference have been both intensively and extensively developed during recent years. Because of these developments, interest in dynamic programming and Bayesian inference and their applications has greatly increased at all mathematical levels. The purpose of this book is to provide some applications of Bayesian optimization and dynamic programming

Analysis of futures and spot electricity markets under risk aversion.

We analyze the procurement problem in the electricity supply chain, focusing on the interaction between futures and spot prices. The supply chain network analyzed in our study includes risk-averse generators and retailers, both with the ability to use conditional value at risk (CV@R) in their decision processes. In this supply chain, the futures price is computed to clear the futures market, without imposing the constraint that the expected spot price equals the futures price. As major methodological contributions: we compute the Nash equilibrium of the problem using CV@R and considering conjectural variations; we derive analytical relationships between the futures and the spot market outcomes and study the implications of demand and marginal cost uncertainty, as well as the level of the players' risk aversion, on market equilibrium; we introduce the concept of risk-adjusted expectation to derive the futures market price as a function of the players' expected losses or profits in the spot market; and we use consistent spot and wholesale price derivatives to calculate the players' reaction functions. Finally, we illustrate our model with several numerical examples in the context of the Spanish electricity market, studying how the shape of the forward curve and the relationship between spot and futures prices depend on seasonality, risk aversion, generators' market power, and hydrological resources. Surprisingly we observed that risk aversion increases the profit and reduces firms' risk, and that the consumer utility is higher in the scenarios in which retailers behave a la Cournot in the wholesale market