Nonconvex optimization for pricing and hedging in imperfect markets.

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).Global optimization; Pseudoarbitrage; Spread reduction; Balance point;

The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms

The Law of One Price (LoOP) states that all firms face the same prices for their inputs and outputs in the competitive market equilibrium. This law has powerful implications for productive efficiency analysis, which have remained unexploited thus far. This paper shows how LoOP-based weight restrictions can be incorporated in Data Envelopment Analysis (DEA). Utilizing the relation between the industry level and the firm level cost efficiency measures, we propose to apply a set of input prices that is common for all firms and that maximizes cost efficiency of the industry. Our framework allows for firm-specific output weights and variable returns-to-scale, and preserves the linear programming structure of the standard DEA. We apply the proposed methodology for evaluating research efficiency of economics departments of Dutch Universities. This application shows that the methodology is computationally tractable for practical efficiency analysis, and that it helps in deepening the DEA analysis.Data Envelopment Analysis; Law of One Price; industry-level efficiency; weight restrictions; research efficiency

Flow-based Capacity Allocation in the CEE Electricity Market: Sensitivity Analysis, Multiple Optima, Total Revenue

The paper introduces the mechanism of the Flow-based Capacity Allocation (FBA) method on the electricity market of the Central-Eastern Europe (CEE) Region, proposed by the Central Allocation Office (CAO). The method is a coordinated heterogeneous multi-unit uniform price auction where the allocation is determined by the solution of a linear programming problem. On one hand, the properties of the underlying linear programming problem are discussed: the possibilities of multiple solutions are analysed, then a non-standard sensitivity analysis method of the market spread auction is developed. On the other hand, a global optimization problem is presented that yields uniform auction prices corresponding to higher total income than at the original allocation method. Several numerical examples and results of practical test problems are presented

Optimization as an analysis tool for human complex decision making

We present a problem class of mixed-integer nonlinear programs (MINLPs) with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving. In a round-based scenario participants hold an executive function. A posteriori a performance indicator is calculated and correlated to personal measures such as intelligence, working memory, or emotion regulation. Altogether, we investigate 2088 optimization problems that differ in size and initial conditions, based on real-world experimental data from 12 rounds of 174 participants. The goals are twofold. First, from the optimal solutions we gain additional insight into a complex system, which facilitates the analysis of a participant’s performance in the test. Second, we propose a methodology to automatize this process by providing a new criterion based on the solution of a series of optimization problems. By providing a mathematical optimization model and this methodology, we disprove the assumption that the “fruit fly of complex problem solving,” the Tailorshop scenario that has been used for dozens of published studies, is not mathematically accessible—although it turns out to be extremely challenging even for advanced state-of-the-art global optimization algorithms and we were not able to solve all instances to global optimality in reasonable time in this study. The publicly available computational tool Tobago [TOBAGO web site https://sourceforge.net/projects/tobago] can be used to automatically generate problem instances of various complexity, contains interfaces to AMPL and GAMS, and is hence ideally suited as a testbed for different kinds of algorithms and solvers. Computational practice is reported with respect to the influence of integer variables, problem dimension, and local versus global optimization with different optimization codes

Nonconvex optimization for pricing and hedging in imperfect markets

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).Partially funded by "Comunidad Autónoma de Madrid" and Spanish Ministry of Science and Education (ref: BEC2003-09067 -C04-03).Publicad

Pooling, Pricing and Trading of Risks

Abstract. Exchange of risks is considered here as a transferableutility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced only in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.Keywords: cooperative game; transferable utility; core; risks; mutual insurance; contingent prices; bilateral exchange; supergradients; stochastic approximation.

Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition

In this paper we consider a novel partitioned framework for distributed optimization in peer-to-peer networks. In several important applications the agents of a network have to solve an optimization problem with two key features: (i) the dimension of the decision variable depends on the network size, and (ii) cost function and constraints have a sparsity structure related to the communication graph. For this class of problems a straightforward application of existing consensus methods would show two inefficiencies: poor scalability and redundancy of shared information. We propose an asynchronous distributed algorithm, based on dual decomposition and coordinate methods, to solve partitioned optimization problems. We show that, by exploiting the problem structure, the solution can be partitioned among the nodes, so that each node just stores a local copy of a portion of the decision variable (rather than a copy of the entire decision vector) and solves a small-scale local problem

Concepts of Optimality and Their Uses

Lecture to the memory of Alfred Nobel, December 11, 1975allocation of resources;

Quota and Risk Sharing among Fishermen

Pooling and exchange of random resources may offer the owners insurance and substitution. Greater efficiency and more stable revenues thereby obtain. These good properties derive from a sharing rule that complies with the core concept from cooperative production games. It is applied here to fisheries with stochastic yield.Resource management; randomization; risk; insurance; cooperative games; core allocations; mutual exchange; stochastic programming; communal fisheries.