Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It\^o's formula of Gozzi and Russo (2006) that applies to C^{0,1}-functions of continuous weak Dirichlet processes. It is motivated and illustrated by its applications to the hedging or superhedging problems of path-dependent options in mathematical finance, in particular in the case of model uncertainty

A wide variety of deep reinforcement learning (DRL) models have recently been proposed to learn profitable investment strategies. The rules learned by these models outperform the previous strategies specially in high frequency trading environments. However, it is shown that the quality of the extracted features from a long-term sequence of raw prices of the instruments greatly affects the performance of the trading rules learned by these models. Employing a neural encoder-decoder structure to extract informative features from complex input time-series has proved very effective in other popular tasks like neural machine translation and video captioning in which the models face a similar problem. The encoder-decoder framework extracts highly informative features from a long sequence of prices along with learning how to generate outputs based on the extracted features. In this paper, a novel end-to-end model based on the neural encoder-decoder framework combined with DRL is proposed to learn single instrument trading strategies from a long sequence of raw prices of the instrument. The proposed model consists of an encoder which is a neural structure responsible for learning informative features from the input sequence, and a decoder which is a DRL model responsible for learning profitable strategies based on the features extracted by the encoder. The parameters of the encoder and the decoder structures are learned jointly, which enables the encoder to extract features fitted to the task of the decoder DRL. In addition, the effects of different structures for the encoder and various forms of the input sequences on the performance of the learned strategies are investigated. Experimental results showed that the proposed model outperforms other state-of-the-art models in highly dynamic environments.

Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, it has attracted little attention in streaming settings until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data.

TV serials are a popular source of entertainment. The ongoing COVID19 lockdown has a high probability of degrading the publics mental health. The Government of India started the retelecast of yesteryears popular TV serials on public broadcaster Doordarshan from 28th March 2020 to 31st July 2020. Tweets corresponding to the Doordarshan hashtag were mined to create a dataset. The experiment aims to analyze the publics response to the retelecast of TV serials by calculating the sentiment score of the tweet dataset. Datasets mean sentiment score of 0.65 and high share 64.58% of positive tweets signifies the acceptance of Doordarshans retelecast decision. The sentiment analysis result also reflects the positive state of mind of the public.

We consider the problem of aggregating predictions or measurements from a set of human forecasters, models, sensors or other instruments which may be subject to bias or miscalibration and random heteroscedastic noise. We propose a Bayesian consensus estimator that adjusts for miscalibration and noise and show that this estimator is unbiased and asymptotically more efficient than naive alternatives. We further propose a Hierarchical Bayesian Model that leverages our proposed estimator and apply it to two real world forecasting challenges that require consensus estimates from error prone individual estimates: forecasting influenza like illness (ILI) weekly percentages and forecasting annual earnings of public companies. We demonstrate that our approach is effective at mitigating bias and error and results in more accurate forecasts than existing consensus models.

We study the fundamental differences that separate: Litecoin; Bitcoin Gold; Bitcoin Cash; Ethereum; and Zcash from Bitcoin, and draw analysis to how these features are appreciated by the market, to ultimately make an inference as to how future successful cryptocurrencies may behave. We use Google Trend data, as well as price, volume and market capitalization data sourced from coinmarketcap.com to support this analysis. We find that Litecoin's shorter block times offer benefits in commerce, but drawbacks in the mining process through orphaned blocks. Zcash holds a niche use for anonymous transactions, benefitting areas of the world lacking in economic freedom. Bitcoin Cash suffers from centralization in the mining process, while the greater decentralization of Bitcoin Gold has generally left it to stagnate. Ether's greater functionality offers the greatest threat to Bitcoin's dominance in the market. A coin that incorporates several of these features can be technically better than Bitcoin, but the first-to-marketadvantage of Bitcoin should keep its dominant position in the market.

We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We choose time-dependent parameters of the model so that the integral equation for the exercise boundary can be solved in the closed form. We also define the contracts of put type with time-dependent strike price that support the explicit optimal exercise boundary.

In this study, we will study investor attention measurement using the Search Volume Index in the recent market. Since 2009, the popularity of mobile devices and the spread of the Internet have made the speed of information delivery faster and the investment information retrieval data for obtaining investment information has increased dramatically. In these circumstances, investor attention measurement using search volume data can be measured more accurately and faster than before mobile device popularization. To confirm this, we will compare the effect of measuring investor attention using search volume data before and after mobile device popularization. In addition, it is confirmed that the measured investor attention is that of retail traders, not institutional traders or professional traders, and the relationship between investor attention and short-term price pressure theory. Using SVI data provided by Google Trends, we will experiment with Russell 3000 stocks and IPO stocks and compare the results. In addition, the results of investigating the investor's interest using the search volume data from various angles through experiments such as the comparison of the results based on the inclusion of the noise ticker group, the comparison of the limitations of the existing investor attention measurement method, and the comparison of explanatory variables with existing IPO related studies. We would like to verify its practicality and significance.

The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.

With the recent advancement in Deep Reinforcement Learning in the gaming industry, we are curious if the same technology would work as well for common quantitative financial problems. In this paper, we will investigate if an off-the-shelf library developed by OpenAI can be easily adapted to mean reversion strategy. Moreover, we will design and test to see if we can get better performance by narrowing the function space that the agent needs to search for.We achieve this through augmenting the reward function by a carefully picked penalty term.

The objective of this paper is to verify that current cutting-edge artificial intelligence technology, deep reinforcement learning, can be applied to portfolio management. We improve on the existing Deep Reinforcement Learning Portfolio model and make many innovations. Unlike many previous studies on discrete trading signals in portfolio management, we make the agent to short in a continuous action space, design an arbitrage mechanism based on Arbitrage Pricing Theory,and redesign the activation function for acquiring action vectors, in addition, we redesign neural networks for reinforcement learning with reference to deep neural networks that process image data. In experiments, we use our model in several randomly selected portfolios which include CSI300 that represents the market's rate of return and the randomly selected constituents of CSI500. The experimental results show that no matter what stocks we select in our portfolios, we can almost get a higher return than the market itself. That is to say, we can defeat market by using deep reinforcement learning.

We study identification and estimation of causal effects in settings with panel data. Traditionally researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the unobserved confounders. We focus on a novel, complementary, approach to identification where assumptions are made about the relation between the treatment assignment and the unobserved confounders. We introduce different sets of assumptions that follow the two paths to identification, and develop a double robust approach. We propose estimation methods that build on these identification strategies.

This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories, extremes, and show greater persistence in anomalies over time.

This paper investigates the causal relationship between income shocks during the first years of life and adulthood mortality due to specific causes of death. Using all death records in the United States during 1968-2004 for individuals who were born in the first half of the 20th century, we document a sizable and statistically significant association between income shocks early in life, proxied by GDP per capita fluctuations, and old age cause-specific mortality. Conditional on individual characteristics and controlling for a broad array of current and early-life conditions, we find that a 1 percent decrease in the aggregate business cycle in the year of birth is associated with 2.2, 2.3, 3.1, 3.7, 0.9, and 2.1 percent increase in the likelihood of mortality in old ages due to malignant neoplasms, Diabetes Mellitus, cardiovascular diseases, Influenza, chronic respiratory diseases, and all other diseases, respectively.

An explicit weak solution for the 3/2 stochastic volatility model is obtained and used to develop a simulation algorithm for option pricing purposes. The 3/2 model is a non-affine stochastic volatility model whose variance process is the inverse of a CIR process. This property is exploited here to obtain an explicit weak solution, similarly to Kouritzin (2018). A simulation algorithm based on this solution is proposed and tested via numerical examples. The performance of the resulting pricing algorithm is comparable to that of other popular simulation algorithms.

Investment in research and development is a key factor in increasing countries' competitiveness. However, its impact can potentially be broader and include other socially relevant elements like job quality. In effect, the quantity of generated jobs is an incomplete indicator since it does not allow to conclude on the quality of the job generated. In this sense, this paper intends to explore the relevance of R&D investments for the job quality in the European Union between 2009 and 2018. For this purpose, we investigate the effects of R&D expenditures made by the business sector, government, and higher education sector on three dimensions of job quality. Three research methods are employed, i.e. univariate linear analysis, multiple linear analysis, and cluster analysis. The findings only confirm the association between R&D expenditure and the number of hours worked, such that the European Union countries with the highest R&D expenses are those with the lowest average weekly working hours.

We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem related to the original MV problem, and obtain the optimal strategy and the value function to the new problem in closed-form. We compare our formulation and optimal strategy to those under the precommitment and game-theoretic framework. Numerical studies show that, when the financial market is negatively correlated with the risk process, optimal investment may involve short selling the risky asset and, if that happens, a less risk averse insurer short sells more risky asset.

Indeed, the global production (as a system of creating values) is eventually forming like a gigantic and complex network/web of value chains that explains the transitional structures of global trade and development of the global economy. It's truly a new wave of globalisation, and we term it as the global value chains (GVCs), creating the nexus among firms, workers and consumers around the globe. The emergence of this new scenario asks: how an economy's firms, producers and workers connect in the global economy. And how are they capturing the gains out of it in terms of different dimensions of economic development? This GVC approach is very crucial for understanding the organisation of the global industries and firms. It requires the statics and dynamics of diverse players involved in this complex global production network. Its broad notion deals with different global issues (including regional value chains also) from the top down to the bottom up, founding a scope for policy analysis (Gereffi & Fernandez-Stark 2011). But it is true that, as Feenstra (1998) points out, any single computational framework is not sufficient to quantification this whole range of economic activities. We should adopt an integrative framework for accurate projection of this dynamic multidimensional phenomenon.

Previous studies show that prenatal shocks to embryos could have adverse impacts on health endowment at birth. Using the universe of birth data and a difference-in-difference-in-difference strategy, I find that exposure to Ramadan during prenatal development has negative birth outcomes. Exposure to a full month of fasting is associated with 96 grams lower birth-weight. These results are robust across specifications and do not appear to be driven by mothers selective fertility.

We consider Heston's (1993) stochastic volatility model for valuation of European options to which (semi) closed form solutions are available and are given in terms of characteristic functions. We prove that the class of scale-parameter distributions with mean being the forward spot price satisfies Heston's solution. Thus, we show that any member of this class could be used for the direct risk-neutral valuation of the option price under Heston's SV model. In fact, we also show that any RND with mean being the forward spot price that satisfies Hestons' option valuation solution, must be a member of a scale-family of distributions in that mean. As particular examples, we show that one-parameter versions of the {\it Log-Normal, Inverse-Gaussian, Gamma, Weibull} and the {\it Inverse-Weibull} distributions are all members of this class and thus provide explicit risk-neutral densities (RND) for Heston's pricing model. We demonstrate, via exact calculations and Monte-Carlo simulations, the applicability and suitability of these explicit RNDs using already published Index data with a calibrated Heston model (S\&P500, Bakshi, Cao and Chen (1997), and ODAX, Mr\'azek and Posp\'i\v{s}il (2017)), as well as current option market data (AMD).

According to the World Health Organization, development of the COVID-19 vaccine is occurring in record time. Administration of the vaccine has started the same year as the declaration of the COVID-19 pandemic. The United Nations emphasized the importance of providing COVID-19 vaccines as "a global public good", which is accessible and affordable world-wide. Pricing the COVID-19 vaccines is a controversial topic. We use optimization and game theoretic approaches to model the COVID-19 U.S. vaccine market as a duopoly with two manufacturers Pfizer-BioNTech and Moderna. The results suggest that even in the context of very high production and distribution costs, the government can negotiate prices with the manufacturers to keep public sector prices as low as possible while meeting demand and ensuring each manufacturer earns a target profit. Furthermore, these prices are consistent with those currently predicted in the media.

Research on quantum technology spans multiple disciplines: physics, computer science, engineering, and mathematics. The objective of this manuscript is to provide an accessible introduction to this emerging field for economists that is centered around quantum computing and quantum money. We proceed in three steps. First, we discuss basic concepts in quantum computing and quantum communication, assuming knowledge of linear algebra and statistics, but not of computer science or physics. This covers fundamental topics, such as qubits, superposition, entanglement, quantum circuits, oracles, and the no-cloning theorem. Second, we provide an overview of quantum money, an early invention of the quantum communication literature that has recently been partially implemented in an experimental setting. One form of quantum money offers the privacy and anonymity of physical cash, the option to transact without the involvement of a third party, and the efficiency and convenience of a debit card payment. Such features cannot be achieved in combination with any other form of money. Finally, we review all existing quantum speedups that have been identified for algorithms used to solve and estimate economic models. This includes function approximation, linear systems analysis, Monte Carlo simulation, matrix inversion, principal component analysis, linear regression, interpolation, numerical differentiation, and true random number generation. We also discuss the difficulty of achieving quantum speedups and comment on common misconceptions about what is achievable with quantum computing.

Quantum models based on the mathematics of quantum mechanics (QM) have been developed in cognitive sciences, game theory and econophysics. In this work a generalization of credit loans is introduced by using the vector space formalism of QM. Operators for the debt, amortization, interest and periodic installments are defined and its mean values in an arbitrary orthonormal basis of the vectorial space give the corresponding values at each period of the loan. Endowing the vector space of dimension M, where M is the loan duration, with a SO(M) symmetry, it is possible to rotate the eigenbasis to obtain better schedule periodic payments for the borrower, by using the rotation angles of the SO(M) transformation. Given that a rotation preserves the length of the vectors, the total amortization, debt and periodic installments are not changed. For a general description of the formalism introduced, the loan operator relations are given in terms of a generalized Heisenberg algebra, where finite dimensional representations are considered and commutative operators are defined for the specific loan types. The results obtained are an improvement of the usual financial instrument of credit because introduce several degrees of freedom through the rotation angles, which allows to select superposition states of the corresponding commutative operators that enables the borrower to tune the periodic installments in order to obtain better benefits without changing what the lender earns.

The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a benchmark portfolio over a given time-horizon with probability one. This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the $N$ investors and mean field regimes under some market conditions. An investor competes with a benchmark of market and peer investors, expecting to outperform the benchmark and minimizing the initial capital.

With market price of risk processes depending on the market portfolio and investors, we develop a systematic way to solve multi-agent optimization problem within SPT's framework. The objective can be characterized by the smallest nonnegative continuous solution of a Cauchy problem. By a modification in the structure of the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium, we show a unique equilibrium in $N$-player games and mean field games with mild conditions on the equity market.

We employed the log-periodic power law singularity (LPPLS) methodology to systematically investigate the 2020 stock market crash in the U.S. equities sectors with different levels of total market capitalizations through four major U.S. stock market indexes, including the Wilshire 5000 Total Market index, the S&P 500 index, the S&P MidCap 400 index, and the Russell 2000 index, representing the stocks overall, the large capitalization stocks, the middle capitalization stocks and the small capitalization stocks, respectively. During the 2020 U.S. stock market crash, all four indexes lost more than a third of their values within five weeks, while both the middle capitalization stocks and the small capitalization stocks have suffered much greater losses than the large capitalization stocks and stocks overall. Our results indicate that the price trajectories of these four stock market indexes prior to the 2020 stock market crash have clearly featured the obvious LPPLS bubble pattern and were indeed in a positive bubble regime. Contrary to the popular belief that the COVID-19 led to the 2020 stock market crash, the 2020 U.S. stock market crash was endogenous, stemming from the increasingly systemic instability of the stock market itself. We also performed the complementary post-mortem analysis of the 2020 U.S. stock market crash. Our analyses indicate that the 2020 U.S. stock market crash originated from a bubble which began to form as early as September 2018; and the bubbles in stocks with different levels of total market capitalizations have significantly different starting time profiles. This study not only sheds new light on the making of the 2020 U.S. stock market crash but also creates a novel pipeline for future real-time crash detection and mechanism dissection of any financial market and/or economic index.

In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we prove the averaging principle assuming the sublinearity, the Lipschitzianity and the Holder's continuity in time of the coefficients, an ergodic hypothesis and an $\mathcal{L}^2$-bound of the fast component. In this setting we prove the weak convergence of the slow component to the solution of the averaged equation. Moreover we provide a suitable dissipativity condition under which the ergodic hypothesis and the $\mathcal{L}^2$-bound of the fast component, which are implicit conditions, are satisfied.

In the second part we propose a financial application of this result: we apply the theory developed to a slow-fast local stochastic volatility model. First we prove the weak convergence of the model to a local volatility one. Then under a risk neutral measure we show that the prices of the derivatives, possibly path-dependent, converge to the ones calculated using the limit model.

With the cost of implementation shrinking and the robot-to-workers ratio skyrocketing, the effects of automation on our economy and society are more palpable than ever. Over half of our jobs could be fully executed by machines over the next decade or two, with severe impacts concentrated disproportionately on manufacturing-focused developing countries. In response to the threat of mass displacement of labor due to automation, economists, politicians, and even the business community have come to see Universal Basic Income (UBI) as the panacea. This paper argued against a UBI by addressing its implementation costs and inefficiency in mitigating the impact of automation through quantitative evidence as well as results of failed UBI-comparable programs across the world. The author made a case for the continuation of existing means-tested welfare systems and further investment in education and training schemes for unskilled and low-skilled labor as a more sustainable and effective solution to the automation-induced large-scale displacement of workers.

This paper aims to assess the effects of industrial pollution on infant mortality between the years 1850-1940 using full count decennial censuses. In this period, US economy experienced a tremendous rise in industrial activity with significant variation among different counties in absorbing manufacturing industries. Since manufacturing industries are shown to be the main source of pollution, we use the share of employment at the county level in this industry to proxy for space-time variation in industrial pollution. Since male embryos are more vulnerable to external stressors like pollution during prenatal development, they will face higher likelihood of fetal death. Therefore, we proxy infant mortality with different measures of gender ratio. We show that the upswing in industrial pollution during late nineteenth century and early twentieth century has led to an increase in infant mortality. The results are consistent and robust across different scenarios, measures for our proxies, and aggregation levels. We find that infants and more specifically male infants had paid the price of pollution during upswing in industrial growth at the dawn of the 20th century. Contemporary datasets are used to verify the validity of the proxies. Some policy implications are discussed.

Using the econometric models, this paper addresses the ability of Albanian Small and Medium-sized Enterprises (SMEs) to identify the risks they face. To write this paper, we studied SMEs operating in the Gjirokastra region. First, qualitative data gathered through a questionnaire was used. Next, the 5-level Likert scale was used to measure it. Finally, the data was processed through statistical software SPSS version 21, using the binary logistic regression model, which reveals the probability of occurrence of an event when all independent variables are included. Logistic regression is an integral part of a category of statistical models, which are called General Linear Models. Logistic regression is used to analyze problems in which one or more independent variables interfere, which influences the dichotomous dependent variable. In such cases, the latter is seen as the random variable and is dependent on them. To evaluate whether Albanian SMEs can identify risks, we analyzed the factors that SMEs perceive as directly affecting the risks they face. At the end of the paper, we conclude that Albanian SMEs can identify risk

As more and more data being created every day, all of it can help take better decisions with data analysis. It is not different from data generated in financial markets. Here we examine the process of how the global economy is affected by the market sentiment influenced by the micro-blogging data (tweets) of American President Donald Trump. The news feed is gathered from The Guardian and Bloomberg from the period between December 2016 and October 2019, which are used to further identify the potential tweets that influenced the markets as measured by changes in equity indices.