Introduction to Markets, Policy and Computation Minitrack

N/

A Merchant Transmission Approach for Uniform-Price Electricity Markets

Uniform-price electricity markets as operated in Germany, for instance, rely on a redispatch mechanism after market clearing to ensure the technical feasibility of generation and consumption schedules with regard to grid constraints. This mechanism determines the costs of congestion management and the welfare loss due to the limited transmission capacity. Therefore, the mechanism is suited to incentivize welfare increasing grid expansion. Depending on the distribution of congestion management costs, it can also align stakeholder interests. In this paper, we present an auction mechanism for transmission grid expansion based on the reduction of redispatch expenditures that theoretically leads to a welfare optimal expansion. The mechanism is applied to a case study in Germany. The results show that the developed mechanism supports an improved planning of grid capacity expansion

The Hidden Cost of Priority Dispatch for Wind Power

Renewable generation, such as wind power, is commonly considered a must-take resource in power systems. In this work we show that, given the technical capabilities of current wind turbines, this approach could lead to major economic inefficiency as wind integration levels in power systems increase. We initially provide intuition for cases in which the optimal operating point involves shedding renewable generation, even though no cost is associated with it in the optimization objective, illustrated in small power systems. We then explore the expected benefit from dispatching wind resources at a lower level than their available output in a Stochastic Unit Commitment (SUC) framework. The modeling and evaluation approach adopted are described. A decomposition technique based on recent literature that utilizes global cuts and Lagrangian penalties to achieve convergence is used to solve the resulting large scale mixed integer optimization problem, in a high performance computing environment. A reduced California system is examined as a test case

Essays on the Equity Premium Puzzle

The equity premium puzzle emanates from the inability of the theoretical models to explain the empirically observed high equity premium (when the average stock returns so much higher than the average bond returns). The puzzle is that in order to reconcile the much higher return on stock compared to the return on government bonds in the United States, individuals must have very high (unrealistic) risk aversion according to standard economics models. Mehra and Prescott (1985) [35] found that for high values of relative risk aversion coefficients (=RRA), and a given small variance of the growth rate in the per capita consumption, an Equity Premium puzzle exists. The primary goal of this dissertation is to test different theoretical models, while calibrating their parameters to the data used by Mehra and Prescot (1985) [35], in order to better understand the equity premium puzzle and to find a plausible explanation to that puzzle. I also compare the performance of the models I test with the performance of the models used by Mehra and Prescott (1985) [35] and Constantinides (1990) [11]. The dissertation consists of three essays. In the first essay, I use a model with no time separability of preferences and with habit persistence (= adjacent complementarity in consumption) to try and explain the equity premium puzzle. In addition, and unique to this paper, I represent the stock price movement using a right skewed non-Gaussian model (a skewed Lognormal distribution). I start with defining the model and its assumptions. I then continue with finding the optimal Consumption policy and Investment policy by implementing Ito’s Lemma formulation. Next, I derive the distribution of the subsistence rate of consumption generated by Habit Persistence (z) and use it to calculate the unconditional mean and variance of consumption growth. I then derive the relation between the RRA coefficient and the intertemporal Elasticity of Substitution in Consumption (s). In the final step I examine the Equity Premium puzzle after calibrating the model’s parameter, and then I derive the effect of time separability in utility preferences and Habit persistence on the Equity Premium puzzle. In the second essay, I examine the ability of a dynamic asset-pricing model to explain both the Equity Premium and the Volatility puzzles. I modify the standard asset pricing model in four aspects. First, I use a time varying price of risk (i.e. time varying excess return per unit risk). Second, I incorporate Duesenberry’s demonstration effect and define the Habit formulation that utilizes quasi- ratio consumption. Third, I include tax rates in my model to control for any extreme valuation, relative to GDP, caused by tax rates and not by stock market factors. Fourth, I represent the stock price movement using a right skewed non-Gaussian model (a skewed Lognormal distribution). I utilize the conjecture and verification method to find the form of the state valuation function. After calibrating the model’s parameters, I derive the conditions that enable the Equity Premium puzzle and / or the Volatility puzzle to exist, and then I find the RRA coefficients that meet these conditions. In the third essay, I do not investigate the Equity Premium puzzle. I examine the use of the Finite Element numerical method to price a Double Barrier Knock out European Call Option. I first convert the Black-Scholes partial differential equation into the Heat Equation and then solve it using the Finite Element Method. Numerical experiments are presented to compare the performance of the Finite Element Method with the performance of the Finite Difference Method when pricing the Double Barrier Knock out European Call Option. The dissertation concludes with the role of habit persistence in future economic research paths and in other economics research fields

Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks

In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features for machine learning models. In the context of deep learning models, the FE is embedded in the neural network's architecture, making it hard for interpretation. In this study, we propose to integrate symbolic regression (SR) as an FE process before a machine learning model to improve its performance. We show, through extensive experimentation on synthetic and real-world physics-related datasets, that the incorporation of SR-derived features significantly enhances the predictive capabilities of both machine and deep learning regression models with 34-86% root mean square error (RMSE) improvement in synthetic datasets and 4-11.5% improvement in real-world datasets. In addition, as a realistic use-case, we show the proposed method improves the machine learning performance in predicting superconducting critical temperatures based on Eliashberg theory by more than 20% in terms of RMSE. These results outline the potential of SR as an FE component in data-driven models

Homogenized estimates for soft fiber-composites and tissues with two families of fibers

The macroscopic response of hyperelastic fiber composites is characterized in terms of the behaviors of their constituting phases. To this end, we make use of a unique representation of the deformation gradient in terms of a set of transversely isotropic invariants. Respectively, these invariants correspond to extension along the fibers, transverse dilatation, out-of-plane shear along the fibers, in-plane shear in the transverse plane, and the coupling between the shear modes. With the aid of this representation, it is demonstrated that under a combination of out-of-plane shear and extension along the fibers there is a class of nonlinear materials for which the exact expression for the macroscopic behavior of a composite cylinder assemblage can be determined. The macroscopic response of the composite to shear in the transverse plane is approximated with the aid of an exact result for sequentially laminated composites. Assuming no coupling between the shear modes, these results allow to construct a closed-form homogenized model for the macroscopic response of a fiber composite with neo-Hookean phases. A new variational estimate allows to extend these results to more general classes of materials. The resulting explicit estimates for the macroscopic stresses developing in composites and connective tissues with one and two families of fibers are compared with corresponding finite element simulations of periodic composites and with experimental results. Estimates for the critical stretch ratios at which the composites loose stability at the macroscopic level are compared with the corresponding numerical results too. It is demonstrated that both the primary stress–strain curves and the critical stretch ratios are in fine agreement with the corresponding numerical results