Neural networks for stock price prediction(NNSPP) have been popular for decades. However, most of its study results remain in the research paper and cannot truly play a role in the securities market. One of the main reasons leading to this situation is that the prediction error(PE) based evaluation results have statistical flaws. Its prediction results cannot represent the most critical financial direction attributes. So it cannot provide investors with convincing, interpretable, and consistent model performance evaluation results for practical applications in the securities market. To illustrate, we have used data selected from 20 stock datasets over six years from the Shanghai and Shenzhen stock market in China, and 20 stock datasets from NASDAQ and NYSE in the USA. We implement six shallow and deep neural networks to predict stock prices and use four prediction error measures for evaluation. The results show that the prediction error value only partially reflects the model accuracy of the stock price prediction, and cannot reflect the change in the direction of the model predicted stock price. This characteristic determines that PE is not suitable as an evaluation indicator of NNSPP. Otherwise, it will bring huge potential risks to investors. Therefore, this paper establishes an experiment platform to confirm that the PE method is not suitable for the NNSPP evaluation, and provides a theoretical basis for the necessity of creating a new NNSPP evaluation method in the future.

In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave function on the unit interval. This choice can be motivated by the long term stability of the capital distribution observed in large equity markets, and allows us to circumvent the curse of dimensionality. The resulting optimization problem, which is convex, is flexible as various regularizations and constraints can be imposed on the generating function. We prove that the optimization problem is well-posed and provide a stability estimate in terms of a Wasserstein metric of the input measure. We then give a careful treatment of its discretization and the optimization algorithm. Finally, we present empirical examples using CRSP data from the US stock market.

Nothing has done more to empower the free market, enterprise, and meritocracy than the spread of electricity and power to everyone. The power system has been the precursor to the greatest period of innovation in our history and has meant that visionaries with revolutionary ideas can compete with those with capital, political power, and means. Electricity, therefore, has been the great equalising force of the last 150 years, enhancing the productivity of the masses and granting prosperity to whole swathes of our nation. Whilst electricity has been one of the single largest innovations in enhancing the power of free markets, it is somewhat ironic that the way power is sold to consumers is largely unfree. The market is highly regulated, centralised, and is often used for political football by cynical politicians on both sides of the political spectrum. Introducing Locational Marginal Pricing into the UK grid system will increase economic freedom in the consumer markets for power, reduce prices for the poorest in the UK, decrease transmission losses, increase the permeation of low carbon generation in the grid, and incentivise investment in the UK's Northern Powerhouse initiative.

We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective, and provide a successive convex program algorithm that provides 30 times faster and robust solutions in the experiments. Computational results on the multi-asset universe show that multi-period models perform better than their single period counterparts in out-of-sample period, 2006-2020. The out-of-sample risk-adjusted performance of both mean-variance and risk-parity formulations beat the fix-mix benchmark, and achieve Sharpe ratio of 0.64 and 0.97, respectively.

Modern financial networks are characterized by complex structures of mutual obligations. Such interconnections may propagate and amplificate individual defaults, leading in some cases to financial disaster. For this reason, mathematical models for the study and control of systemic risk (the risk of severe instabilities on the system as a whole, due to default of single entities) have attracted considerable research attention in recent years. One important line of research is concerned with mechanisms of clearing, that is, the mechanism by which mutual debts are repaid, in the regular regime, or in a default regime. One of the first models of a clearing mechanism was proposed by Eisenberg and Noe and is based on the three rules: limited liability, the priority of debt claims over the shareholders' interests, and the equal priority of debts (pro-rata rule). These three principles naturally lead to the concept of clearing vector (the vector of the entities' total payments). In this paper, we propose a necessary and sufficient condition for the uniqueness of clearing vector applicable to an arbitrary topology of the financial network. Further, we show that the overall system loss can be reduced if one relaxes the pro-rata rule and replaces the clearing vector by a matrix of clearing payments. This approach shifts the focus from the individual interest to the system, or social, interest, in order to control and contain the adverse effects of cascaded failures.

This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision-makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized to incorporate effects such as interference and entanglement that characterise human decision-making. Applications to some common problems in economics and finance are discussed.

As a fundamental problem in algorithmic trading, order execution aims at fulfilling a specific trading order, either liquidation or acquirement, for a given instrument. Towards effective execution strategy, recent years have witnessed the shift from the analytical view with model-based market assumptions to model-free perspective, i.e., reinforcement learning, due to its nature of sequential decision optimization. However, the noisy and yet imperfect market information that can be leveraged by the policy has made it quite challenging to build up sample efficient reinforcement learning methods to achieve effective order execution. In this paper, we propose a novel universal trading policy optimization framework to bridge the gap between the noisy yet imperfect market states and the optimal action sequences for order execution. Particularly, this framework leverages a policy distillation method that can better guide the learning of the common policy towards practically optimal execution by an oracle teacher with perfect information to approximate the optimal trading strategy. The extensive experiments have shown significant improvements of our method over various strong baselines, with reasonable trading actions.