I demonstrate that with the market return determined by the equilibrium returns of the CAPM, expected returns of an asset are affected by the risks of all assets jointly. Another implication is that the range of feasible market returns will be limited and dependent on the distribution of weights in the market portfolio. A large and well diversified market with no dominating asset will only return zero while a market dominated by a small number of assets will only return the risk-free rate. In the limiting case of atomistic assets, we recover the properties of the standard CAPM.

It is a difficult task for both professional investors and individual traders continuously making profit in stock market. With the development of computer science and deep reinforcement learning, Buy\&Hold (B\&H) has been oversteped by many artificial intelligence trading algorithms. However, the information and process are not enough, which limit the performance of reinforcement learning algorithms. Thus, we propose a parallel-network continuous quantitative trading model with GARCH and PPO to enrich the basical deep reinforcement learning model, where the deep learning parallel network layers deal with 3 different frequencies data (including GARCH information) and proximal policy optimization (PPO) algorithm interacts actions and rewards with stock trading environment. Experiments in 5 stocks from Chinese stock market show our method achieves more extra profit comparing with basical reinforcement learning methods and bench models.

A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda-Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime.

The performance of a cross-sectional currency strategy depends crucially on accurately ranking instruments prior to portfolio construction. While this ranking step is traditionally performed using heuristics, or by sorting outputs produced by pointwise regression or classification models, Learning to Rank algorithms have recently presented themselves as competitive and viable alternatives. Despite improving ranking accuracy on average however, these techniques do not account for the possibility that assets positioned at the extreme ends of the ranked list -- which are ultimately used to construct the long/short portfolios -- can assume different distributions in the input space, and thus lead to sub-optimal strategy performance. Drawing from research in Information Retrieval that demonstrates the utility of contextual information embedded within top-ranked documents to learn the query's characteristics to improve ranking, we propose an analogous approach: exploiting the features of both out- and under-performing instruments to learn a model for refining the original ranked list. Under a re-ranking framework, we adapt the Transformer architecture to encode the features of extreme assets for refining our selection of long/short instruments obtained with an initial retrieval. Backtesting on a set of 31 currencies, our proposed methodology significantly boosts Sharpe ratios -- by approximately 20% over the original LTR algorithms and double that of traditional baselines.

Calcium (Ca) requirement increases tenfold upon parturition in dairy cows & buffaloes and its deficiency leads to a condition called milk fever (MF). Estimation of losses is necessary to understand the depth of the problem and design preventive measures. How much is the economic loss due to MF? What will be the efficiency gain if MF is prevented at the advent of a technology? We answer these questions using survey data and official statistics employing economic surplus model. MF incidence in sample buffaloes and cows was 19% and 28%, respectively. Total economic losses were calculated as a sum total of losses from milk production, mortality of animals and treatment costs. Yearly economic loss due to MF was estimated to be INR 1000 crores (US$ 137 million) in Haryana. Value of milk lost had the highest share in total economic losses (58%), followed by losses due to mortality (29%) and treatment costs (13%). Despite lower MF incidence, losses were higher in buffaloes due to higher milk prices and market value of animals. The efficiency gain accruing to producers if MF is prevented, resulting from increased milk production at decreased costs was estimated at INR 10990 crores (US$ 1.5 billion). As the potential gain if prevented is around 10 times the economic losses, this study calls for the use of preventive technology against MF.

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical stochastic multiplicative process for non-stationary and non-ergodic dynamics. Resetting is a sudden interruption of a process, which consecutively renews its dynamics. We show that, although resetting renders GBM stationary, the resulting process remains non-ergodic. Quite surprisingly, the effect of resetting is pivotal in manifesting the non-ergodic behavior. In particular, we observe three different long-time regimes: a quenched state, an unstable and a stable annealed state depending on the resetting strength. Notably, in the last regime, the system is self-averaging and thus the sample average will always mimic ergodic behavior establishing a stand alone feature for GBM under resetting. Crucially, the above-mentioned regimes are well separated by a self-averaging time period which can be minimized by an optimal resetting rate. Our results can be useful to interpret data emanating from stock market collapse or reconstitution of investment portfolios.

This exercise offers an innovative learning mechanism to model economic agent's decision making process using a deep reinforcement learning algorithm. In particular, this AI agent has limited or no information on the underlying economic structure and its own preference. I model how the AI agent learns in terms of how it collects and processes information. It is able to learn in real time through constantly interacting with the environment and adjusting its actions accordingly. I illustrate that the economic agent under deep reinforcement learning is adaptive to changes in a given environment in real time. AI agents differ in their ways of collecting and processing information, and this leads to different learning behaviours and welfare distinctions. The chosen economic structure can be generalised to other decision making processes and economic models.

We design multi-horizon forecasting models for limit order book (LOB) data by using deep learning techniques. Unlike standard structures where a single prediction is made, we adopt encoder-decoder models with sequence-to-sequence and Attention mechanisms, to generate a forecasting path. Our methods achieve comparable performance to state-of-art algorithms at short prediction horizons. Importantly, they outperform when generating predictions over long horizons by leveraging the multi-horizon setup. Given that encoder-decoder models rely on recurrent neural layers, they generally suffer from a slow training process. To remedy this, we experiment with utilising novel hardware, so-called Intelligent Processing Units (IPUs) produced by Graphcore. IPUs are specifically designed for machine intelligence workload with the aim to speed up the computation process. We show that in our setup this leads to significantly faster training times when compared to training models with GPUs.

Transition probability densities are fundamental to option pricing. Advancing recent work in deep learning, we develop novel transition density function generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions, using neural networks to obtain accurate approximations of transition probability densities, creating ultra-fast transition density function generators offline that can be trained for any underlying. These are 'single solve' , so they do not require recalculation when parameters are changed (e.g. recalibration of volatility) and are portable to other option pricing setups as well as to less powerful computers, where they can be accessed as quickly as closed-form solutions. We demonstrate the range of application for one-dimensional cases, exemplified by the Black-Scholes-Merton model, two-dimensional cases, exemplified by the Heston process, and finally for a modified Heston model with time-dependent parameters that has no closed-form solution.

Pravuil is a robust, secure, and scalable consensus protocol for a permissionless blockchain suitable for deployment in an adversarial environment such as the Internet. Pravuil circumvents previous shortcomings of other blockchains:

- Bitcoin's limited adoption problem: as transaction demand grows, payment confirmation times grow much lower than other PoW blockchains

- higher transaction security at a lower cost

- more decentralisation than other permissionless blockchains

- impossibility of full decentralisation and the blockchain scalability trilemma: decentralisation, scalability, and security can be achieved simultaneously

- Sybil-resistance for free implementing the social optimum

- Pravuil goes beyond the economic limits of Bitcoin or other PoW/PoS blockchains, leading to a more valuable and stable crypto-currency

In order to study the phenomenon of regional economic development and urban expansion from the perspective of night-light remote sensing images, researchers use NOAA-provided night-light remote sensing image data (data from 1992 to 2013) along with ArcGIS software to process image information, obtain the basic pixel information data of specific areas of the image, and analyze these data from the space-time domain for presentation of the trend of regional economic development in China in recent years, and tries to explore the urbanization effect brought by the rapid development of China's economy. Through the analysis and study of the data, the results show that the urbanization development speed in China is still at its peak, and has great development potential and space. But at the same time, people also need to pay attention to the imbalance of regional development.

Using Forbes 400 data together with historical data on tax rates and macroeconomic indicators, we study the relationship between the maximum marginal income tax rate and wealth inequality. We find through a novel tail regression model that a higher maximum tax rate is associated with a higher wealth Pareto exponent. Setting the maximum rate to 0.30-0.40 (as in U.S. currently) leads to an exponent of 1.5-1.8, while counterfactually setting it to 0.8 (as suggested by Piketty, 2014) would lead to an exponent of 2.6. We present a simple economic model that explains these findings and discuss the welfare implications of taxation.

Telecom industry is significantly evolving all over the globe than ever. Mobile users number is increasing remarkably. Telecom operators are investing to get more users connected and to improve user experience, however, they are facing various challenges. Decrease of main revenue streams of voice calls, SMS (Short Message Service) and LDC (Long distance calls) with a significant increase in data traffic. In contrary, with free cost, OTT (Over the top) providers such as WhatsApp and Facebook communication services rendered over networks that built and owned by MNOs. Recently, OTT services gradually substituting the traditional MNOs` services and became ubiquitous with the help of the underlying data services provided by MNOs. The OTTs` services massive penetration into telecom industry is driving the MNOs to reconsider their strategies and revenue sources.

The purpose of this study is to examine the impact of board member composition and board members' social media presence on the performance of startups. Using multiple sources, we compile a unique dataset of about 500 US-based technology startups. We find that startups with more venture capitalists on the board and whose board members are active on Twitter attract additional funding over the years, though they do not generate additional sales. By contrast, startups which have no venture capitalists on the board and whose board members are not on Twitter show an increased ability to translate assets into sales. Consistent with other research, our results indicate that startups potentially benefit from working with VCs because of the opportunity to access additional funding, although their presence does not necessarily translate into sales growth and operational efficiency. We use a number of control variables, including board gender representation and board members' position in the interlocking directorates' network.

In this paper, we study the behavior of information ratio (IR) as determined by the fundamental law of active investment management. We extend the classic relationship between IR and its two determinants (i.e., information coefficient and investment "breadth") by explicitly and simultaneously taking into account the volatility of IC and the cost from portfolio turnover. Through mathematical derivations and simulations, we show that - for both mean-variance and quintile portfolios - a turnover-adjusted IR is always lower than an IR that ignores the cost from turnover; more importantly, we find that, contrary to the implication from the fundamental low but consistent with available empirical evidence, investment managers may improve their investment performance or IR by limiting/optimizing trade or portfolio turnover.