We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations, in the special case where the interaction matrix is of unit rank, corresponding to a single-resource MacArthur model. We compute the average number of solutions and show that its logarithm grows as $N^\alpha$, where $N$ is the number of assets or species and $\alpha \leq 2/3$ depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity $m(N)$ of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number "satisficing" solutions.

Forecasting the CBOE volatility index (VIX) is a highly non-linear and memory-intensive task. In this paper, we use quantum reservoir computing to forecast the VIX using S&P500 (SPX) time-series. Our reservoir is a hybrid quantum-classical system executed on IBM's 53-qubit Rochester chip. We encode the SPX values in the rotation angles and linearly combine the average spin of the six-qubit register to predict the value of VIX at the next time step. Our results demonstrate a potential application of noisy intermediate scale quantum (NISQ) devices to complex, real world applications.

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We also reduce the dimension of the problem by classifying banks according to different types, in an appropriate type space. These types may be calibrated to real-world data by using machine learning techniques. We then state various limit theorems regarding the final size of default cascade over different types. In particular, under suitable assumptions on the degree and threshold distributions, we show that the final size of default cascade has asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions and show how the systemic risk measure, in a given stress test scenario, could be related to the structure and heterogeneity of financial networks. We finally show how these results could be used by a social planner to optimally target interventions during a financial crisis, with a budget constraint and under partial information of the financial network.

In contrast to the analytic approach to risk for Markov chains based on transition risk mappings, we introduce a probabilistic setting based on a novel concept of regular conditional risk mapping with Markov update rule. We confirm that the Markov property holds for the standard measures of risk used in practice such as Value at Risk and Average Value at Risk. We analyse the dual representation for convex Markovian risk mappings and a representation in terms of their acceptance sets. The Markov property is formulated in several equivalent versions including a strong version, opening up additional risk-sensitive optimisation problems such as optimal stopping with exercise lag and optimal prediction. We demonstrate how such problems can be reduced to a risk-sensitive optimal stopping problem with intermediate costs, and derive the dynamic programming equations for the latter. Finally, we show how our results can be extended to partially observable Markov processes.

The price clustering phenomenon manifesting itself as an increased occurrence of specific prices is widely observed and well-documented for various financial instruments and markets. In the literature, however, it is rarely incorporated into price models. We consider that there are several types of agents trading only in specific multiples of the tick size resulting in an increased occurrence of these multiples in prices. For example, stocks on the NYSE and NASDAQ exchanges are traded with precision to one cent but multiples of five cents and ten cents occur much more often in prices. To capture this behavior, we propose a discrete price model based on a mixture of double Poisson distributions with dynamic volatility and dynamic proportions of agent types. The model is estimated by the maximum likelihood method. In an empirical study of DJIA stocks, we find that higher instantaneous volatility leads to weaker price clustering at the ultra-high frequency. This is in sharp contrast with results at low frequencies which show that daily realized volatility has a positive impact on price clustering.

We argue for a foundational epistemic claim and a hypothesis about the production and uses of mathematical epidemiological models, exploring the consequences for our political and socio-economic lives. First, in order to make the best use of scientific models, we need to understand why models are not truly representational of our world, but are already pitched towards various uses. Second, we need to understand the implicit power relations in numbers and models in public policy, and, thus, the implications for good governance if numbers and models are used as the exclusive drivers of decision making.

We examine probabilistic forecasts for battleground states in the 2020 US presidential election, using daily data from two sources over seven months: a model published by The Economist, and prices from the PredictIt exchange. We find systematic differences in accuracy over time, with markets performing better several months before the election, and the model performing better as the election approached. A simple average of the two forecasts performs better than either one of them overall, even though no average can outperform both component forecasts for any given state-date pair. This effect arises because the model and the market make different kinds of errors in different states: the model was confidently wrong in some cases, while the market was excessively uncertain in others. We conclude that there is value in using hybrid forecasting methods, and propose a market design that incorporates model forecasts via a trading bot to generate synthetic predictions. We also propose and conduct a profitability test that can be used as a novel criterion for the evaluation of forecasting performance.

An important class of structural models investigates the determinants of skill formation and the optimal timing of interventions. To achieve point identification of the parameters, researcher typically normalize the scale and location of the unobserved skills. This paper shows that these seemingly innocuous restrictions can severely impact the interpretation of the parameters and counterfactual predictions. For example, simply changing the units of measurements of observed variables might yield ineffective investment strategies and misleading policy recommendations. To tackle these problems, this paper provides a new identification analysis, which pools all restrictions of the model, characterizes the identified set of all parameters without normalizations, illustrates which features depend on these normalizations, and introduces a new set of important policy-relevant parameters that are identified under weak assumptions and yield robust conclusions. As a byproduct, this paper also presents a general and formal definition of when restrictions are truly normalizations.

Plagiarism is the representation of another author's language, thoughts, ideas, or expressions as one's own original work. In educational contexts, there are differing definitions of plagiarism depending on the institution. Prominent scholars of plagiarism include Rebecca Moore Howard, Susan Blum, Tracey Bretag, and Sarah Elaine Eaton, among others. Plagiarism is considered a violation of academic integrity and a breach of journalistic ethics. It is subject to sanctions such as penalties, suspension, expulsion from school or work, substantial fines and even incarceration. Recently, cases of "extreme plagiarism" have been identified in academia. The modern concept of plagiarism as immoral and originality as an ideal emerged in Europe in the 18th century, particularly with the Romantic movement. Generally, plagiarism is not in itself a crime, but like counterfeiting fraud can be punished in a court for prejudices caused by copyright infringement, violation of moral rights, or torts. In academia and industry, it is a serious ethical offense. Plagiarism and copyright infringement overlap to a considerable extent, but they are not equivalent concepts, and many types of plagiarism do not constitute copyright infringement, which is defined by copyright law and may be adjudicated by courts. Plagiarism might not be the same in all countries. Some countries, such as India and Poland, consider plagiarism to be a crime, and there have been cases of people being imprisoned for plagiarizing. In other instances plagiarism might be the complete opposite of "academic dishonesty," in fact some countries find the act of plagiarizing a professional's work flattering. Students who move to the United States and other Western countries from countries where plagiarism is not frowned upon often find the transition difficult.

Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. These trades impose costs on Liquidity Providers (LPs) who supply reserves to CFMMs. Trading fees have been proposed as a mechanism for compensating LPs for arbitrage losses. However, large fees reduce the accuracy of the prices reported by CFMMs and can cause reserves to deviate from desirable asset compositions. CFMM designers are therefore faced with the problem of how to optimally select fees to attract liquidity. We develop a framework for determining the value to LPs of supplying liquidity to a CFMM with fees when the underlying process follows a general diffusion. Focusing on a popular class of CFMMs which we call Geometric Mean Market Makers (G3Ms), our approach also allows one to select optimal fees for maximizing LP value. We illustrate our methodology by showing that an LP with mean-variance utility will prefer a G3M over all alternative trading strategies as fees approach zero.

We develop an arbitrage-free random field LIBOR market model to price cross-currency derivatives. The uncertainty of the forward LIBOR rates of our cross-currency model is driven by a two time parameter random field instead of a finite dimensional Brownian motion. To demonstrate the applications of this model, we develop an approximate closed-form pricing formula for Quanto caps and cross-currency swaps. Further, we derive an exact pricing formula for an exchange rate option in the random field setting.

Tis paper is a literature review focusing on human capital, skills of employees, demographic change, management, training and their impact on productivity growth. Intrafirm behaviour has been recognized as a potentially important driver for productivity. Results from surveys show that management practices have become more structured, in the sense of involving more data collection and analysis. Furthermore, a strong positive correlation between the measured management quality and firm performance can be observed. Studies suggest that there is a positive association between management score and productivity growth. The lack or low level of employees' skills and qualifications might be in different ways a possible explanation for the observed slowdown of productivity growth. The main reason for the decline in skilled labor is the demographic change. Construction sectors are increasingly affected by demographic developments. Labour reserves in construction are largely exhausted. Shortage of qualified workforce is impacting project cost, schedules and quality.

Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider binomially distributed variables in the example of medication testing with fixed placebo efficacy, asking how many experiments are needed in order to achieve a significance of 95 %. In the next step, we take the probability distribution of the placebo efficacy into account, which to the best of our knowledge has not been done so far. Depending on the specifics, we show that in order to obtain identical significance, it may be necessary to perform twice as many experiments than in a setting where the placebo distribution is neglected. We proceed by considering more general probability distributions and close with comments on some erroneous assumptions on probability distributions which lead, for instance, to a trivial explanation of the fat tail.

In recent decades, the male-female wage gap has fallen, while the skilled-unskilled wage gap has risen in advanced countries. The rate of decline in the gender wage gap tends to be greater for unskilled than skilled workers, while the rate of increase in the skill wage gap tends to be greater for male than female workers. To account for these trends, we develop an aggregate production function extended to allow for gender-specific capital-skill complementarity, and estimate it using shift-share instruments and cross-country panel data from OECD countries. We confirm that ICT equipment is more complementary not only to skilled than unskilled workers but also to female than male workers. Our results show that changes in gender and skill premia can be explained in terms of the race between progress in ICT and advances in educational attainment and female employment. In addition, we examine the implications of gender-specific capital-skill complementarity for changes in the labor share of income.

Using the method of Haberis and Lipinska (2020), this paper explores the effect of forward guidance (FG) in a two-country New Keynesian (NK) economy under the zero lower bound (ZLB). We simulate the effect of different lengths of FG or the zero interest rate policy under the circumstance of the global liquidity trap. We show that the size of the intertemporal elasticity of substitution plays an important role in determining the beggar-thy-neighbor effect or the prosper-thy-neighbor effect of home FG policy on the foreign economy. And in the former case, by targeting a minimum welfare loss of the individual country alone but not global welfare loss, two central banks can perform interesting FG bargaining in which they cooperatively adopt the same length of FG or strategically deviate from cooperation.

Advances in Reinforcement Learning (RL) span a wide variety of applications which motivate development in this area. While application tasks serve as suitable benchmarks for real world problems, RL is seldomly used in practical scenarios consisting of abrupt dynamics. This allows one to rethink the problem setup in light of practical challenges. We present Trade Execution using Reinforcement Learning (TradeR) which aims to address two such practical challenges of catastrophy and surprise minimization by formulating trading as a real-world hierarchical RL problem. Through this lens, TradeR makes use of hierarchical RL to execute trade bids on high frequency real market experiences comprising of abrupt price variations during the 2019 fiscal year COVID19 stock market crash. The framework utilizes an energy-based scheme in conjunction with surprise value function for estimating and minimizing surprise. In a large-scale study of 35 stock symbols from the S&P500 index, TradeR demonstrates robustness to abrupt price changes and catastrophic losses while maintaining profitable outcomes. We hope that our work serves as a motivating example for application of RL to practical problems.