# Research articles for the 2021-04-18

Bandits in Matching Markets: Ideas and Proposals for Peer Lending
Soumajyoti Sarkar
arXiv

Motivated by recent applications of sequential decision making in matching markets, in this paper we attempt at formulating and abstracting market designs for P2P lending. We describe a paradigm to set the stage for how peer to peer investments can be conceived from a matching market perspective, especially when both borrower and lender preferences are respected. We model these specialized markets as an optimization problem and consider different utilities for agents on both sides of the market while also understanding the impact of equitable allocations to borrowers. We devise a technique based on sequential decision making that allow the lenders to adjust their choices based on the dynamics of uncertainty from competition over time and that also impacts the rewards in return for their investments. Using simulated experiments we show the dynamics of the regret based on the optimal borrower-lender matching and find that the lender regret depends on the initial preferences set by the lenders which could affect their learning over decision making steps.

Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity
arXiv

The so-called Benford's laws are of frequent use in order to observe anomalies and regularities in data sets, in particular, in election results and financial statements. Yet, basic financial market indices have not been much studied, if studied at all, within such a perspective. This paper presents features in the distributions of S\&P500 daily closing values and the corresponding daily log returns over a long time interval, [03/01/1950 - 22/08/2014], amounting to 16265 data points. We address the frequencies of the first, second, and first two significant digits counts and explore the conformance to Benford's laws of these distributions at five different (equal size) levels of disaggregation. The log returns are studied for either positive or negative cases. The results for the S&P500 daily closing values are showing a huge lack of non-conformity, whatever the different levels of disaggregation. Some "first digits" and "first two digits" values are even missing. The causes of this non-conformity are discussed, pointing to the danger in taking Benford's laws for granted in huge databases, whence drawing "definite conclusions". The agreements with Benford's laws are much better for the log returns. Such a disparity in agreements finds an explanation in the data set itself: the inherent trend in the index. To further validate this, daily returns have been simulated calibrating the simulations with the observed data averages and tested against Benford's laws. One finds that not only the trend but also the standard deviation of the distributions are relevant parameters in concluding about conformity with Benford's laws.

Contribui\c{c}\~ao do ecoturismo para o uso sustent\'avel dos recursos h\'idricos do munic\'ipio de Rondon\'opolis-MT
Manoel Benedito Nirdo da Silva Campos
arXiv

The Municipality of Rondon\'opolis possesses several touristic attractions such as a great diversity of waterfalls and little beaches located in the surroundings of the urban area, which attract tourists from various locations. Aiming to understand how ecotourism can contribute to the conservation of water resources in the leisure areas, as well as their potential development of touristic activities in those places. The procedures included the use of various techniques subsidized in remote sensing and geoprocessing tools that allowed the analysis and spatial distribution of tourism activities of the main leisure areas. The spatial distribution of the waterfalls and its surroundings, we observe the biophysical characters such as: the endemic vegetation, the cachoeiras, the waterfalls, the rocky outcrops, rivers, little beaches and espraiados. The results showed a correct perception of respondents on existing inter-relationships between ecotourism practices and the sustainable use of water resources. In conclusion though, a long way must be performed in order to prevent the economic benefits of ecotourism generate an inappropriate exploitation of natural resources, causing environmental problems, particularly to water resources in the surroundings.

Exploratory Data Analysis of Electric Tricycle as Sustainable Public Transport Mode in General Santos City Using Logistic Regression
Geoffrey L. Cueto,Francis Aldrine A. Uy,Keith Anshilo Diaz
arXiv

General Santos City, as the tuna capital of the Philippines, relies with the presence of tricycles in moving people and goods. Considered as a highly-urbanized city, General Santos City serves as vital link of the entire SOCKSARGEN region's economic activities. With the current thrust of the city in providing a sustainable transport service, several options were identified to adopt in the entire city, that includes cleaner and better transport mode. Electric tricycle is an after sought alternative that offers better choice in terms of identified factors of sustainable transport: reliability, safety, comfort, environment, affordability, and facility. A literature review was conducted to provide a comparison of cost and emission between a motorized tricycle and an e-tricycle. The study identified the existing tricycle industry of the city and reviewed the modal share with the city's travel pattern. The survey revealed a number of hazards were with the current motorized tricycle that needs to address for the welfare of the passengers and drivers. The study favors the shift to adopting E-tricycle. The model derived from binary logistics regression provided a 72.72% model accuracy. Based from the results and findings, electric tricycle can be an alternative mode of public transport in the city that highly support sustainable option that provides local populace to improve their quality of life through mobility and economic activity. Further recommendation to local policy makers in the transport sector of the city include the clustering of barangays for better traffic management and franchise regulation, the inclusion of transport-related infrastructure related to tricycle service with their investment planning and programming, the roll out and implementation of tricycle code of the city, and the piloting activity of introducing e-tricycle in the city.

Improving Transparency in IDIQ Contracts: A Comparison of Common Procurement Issues Affecting Economies Across the Atlantic and Suggested Solutions
Sareesh Rawat
arXiv

Expansions in the size and scope of public procurement across the Atlantic have increased calls for accountability of democratic governments. Indefinite Delivery, Indefinite Quantity contracts by their very nature are less transparent but serve as major tools of public procurement in both the European and American economies. This paper utilizes a cross-Atlantic perspective to discuss common challenges faced by governments and contracting entities while highlighting the need for balancing transparency with efficiency to avoid negative economic outcomes. It concludes by discussing and providing potential solutions to certain common challenges.

Micro-Estimates of Wealth for all Low- and Middle-Income Countries
Guanghua Chi,Han Fang,Sourav Chatterjee,Joshua E. Blumenstock
arXiv

Many critical policy decisions, from strategic investments to the allocation of humanitarian aid, rely on data about the geographic distribution of wealth and poverty. Yet many poverty maps are out of date or exist only at very coarse levels of granularity. Here we develop the first micro-estimates of wealth and poverty that cover the populated surface of all 135 low and middle-income countries (LMICs) at 2.4km resolution. The estimates are built by applying machine learning algorithms to vast and heterogeneous data from satellites, mobile phone networks, topographic maps, as well as aggregated and de-identified connectivity data from Facebook. We train and calibrate the estimates using nationally-representative household survey data from 56 LMICs, then validate their accuracy using four independent sources of household survey data from 18 countries. We also provide confidence intervals for each micro-estimate to facilitate responsible downstream use. These estimates are provided free for public use in the hope that they enable targeted policy response to the COVID-19 pandemic, provide the foundation for new insights into the causes and consequences of economic development and growth, and promote responsible policymaking in support of the Sustainable Development Goals.

Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering
Calypso Herrera,Florian Krach,Josef Teichmann
arXiv

Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical guarantees for their predictive capabilities are available. Assuming that the irregularly-sampled time series data originates from a continuous stochastic process, the $L^2$-optimal online prediction is the conditional expectation given the currently available information. We introduce the Neural Jump ODE (NJ-ODE) that provides a data-driven approach to learn, continuously in time, the conditional expectation of a stochastic process. Our approach models the conditional expectation between two observations with a neural ODE and jumps whenever a new observation is made. We define a novel training framework, which allows us to prove theoretical guarantees for the first time. In particular, we show that the output of our model converges to the $L^2$-optimal prediction. This can be interpreted as solution to a special filtering problem. We provide experiments showing that the theoretical results also hold empirically. Moreover, we experimentally show that our model outperforms the baselines in more complex learning tasks and give comparisons on real-world datasets.

Neural networks-based algorithms for stochastic control and PDEs in finance
Maximilien Germain,Huyên Pham,Xavier Warin
arXiv

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and derivative pricing in financial engineering. We survey recent results in the literature, present new developments, notably in the fully nonlinear case, and compare the different schemes illustrated by numerical tests on various financial applications. We conclude by highlighting some future research directions.

Optimal Algorithmic Monetary Policy
Luyao Zhang,Yulin Liu
arXiv

Centralized monetary policy, leading to persistent inflation, is often inconsistent, untrustworthy, and unpredictable. Algorithmic stable coins enabled by blockchain technology are promising in solving this problem. Algorithmic stable coins utilize a monetary policy that is entirely rule-based. However, there is little understanding about how to optimize the rule. We propose a model that trade-offs between the price and supply stability. We further study the comparative statistics by varying several design features. Finally, we discuss the empirical implications and further research for industry applications.

Ordered Risk Aggregation under Dependence Uncertainty
Yuyu Chen,Liyuan Lin,Ruodu Wang
arXiv

We study the aggregation of two risks when the marginal distributions are known and the dependence structure is unknown, under the additional constraint that one risk is no larger than the other. Risk aggregation problems with the order constraint are closely related to the recently introduced notion of the directional lower (DL) coupling. The largest aggregate risk in concave order (thus, the smallest aggregate risk in convex order) is attained by the DL coupling. These results are further generalized to calculate the best-case and worst-case values of tail risk measures. In particular, we obtain analytical formulas for bounds on Value-at-Risk. Our numerical results suggest that the new bounds on risk measures with the extra order constraint can greatly improve those with full dependence uncertainty.

Power-law Portfolios
Jan Rosenzweig
arXiv

Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to the non-Gaussianity of portfolio returns. \\ In order to look at optimal portfolios for arbitrary risk penalty functions, we construct portfolio shapes where the penalty is proportional to a moment of the returns of arbitrary order $p>2$. \\ The resulting component weight in the portfolio scales sub-linearly with its return, with the power-law $w \propto \mu^{1/(p-1)}$. This leads to significantly improved diversification when compared to Kelly portfolios, due to the dilution of the winner-takes-all effect.\\ In the limit of penalty order $p\rightarrow\infty$, we recover the simple trading heuristic whereby assets are allocated a fixed positive weight when their return exceeds the hurdle rate, and zero otherwise. Infinite order power-law portfolios thus fall into the class of perfectly diversified portfolios.

Removing non-smoothness in solving Black-Scholes equation using a perturbation method
Endah R.M. Putri,Lutfi Mardianto,Amirul Hakam,Chairul Imron,Hadi Susanto
arXiv

Black-Scholes equation as one of the most celebrated mathematical models has an explicit analytical solution known as the Black-Scholes formula. Later variations of the equation, such as fractional or nonlinear Black-Scholes equations, do not have a closed form expression for the corresponding formula. In that case, one will need asymptotic expansions, including homotopy perturbation method, to give an approximate analytical solution. However, the solution is non-smooth at a special point. We modify the method by {first} performing variable transformations that push the point to infinity. As a test bed, we apply the method to the solvable Black-Scholes equation, where excellent agreement with the exact solution is obtained. We also extend our study to multi-asset basket and quanto options by reducing the cases to single-asset ones. Additionally we provide a novel analytical solution of the single-asset quanto option that is simple and different from the existing expression.

The Struggle with Inequality
Shin-Ichiro Inaba
arXiv

This is an introductory textbook of the history of economics of inequality for undergraduates and genreral readers. It begins with Adam Smith's critique of Rousseau. The first and second chapters focus on Smith and Karl Marx, in the broad classical tradition of economics, where it is believed that there is an inseparable relationship between production and distribution, economic growth and inequality. Chapters 3 and 4 argue that despite the fact that the founders of the neoclassical school had shown an active interest in social issues, namely worker poverty, the issues of production and distribution became discussed separately among neoclassicals. Toward the end of the 20th century, however, there was a renewed awareness within economics of the problem of the relationship between production and distribution. The young Piketty's beginnings as an economist are set against this backdrop. Chapters 5 to 8 explain the circumstances of the restoration of classical concerns within the neoclassical framework. Then, in chapters 9 and 10, I discuss the fact that Thomas Piketty's seminal work is a new development in this "inequality renaissance," and try to gain a perspective on future trends in the debate. Mathematical appendix presents simple models of growth and distribution.

The spatial dissemination of COVID-19 and associated socio-economic consequences
Yafei Zhang,Lin Wang,Jonathan J. H. Zhu,Xiaofan Wang
arXiv

The ongoing coronavirus disease 2019 (COVID-19) pandemic has wreaked havoc worldwide with millions of lives claimed, human travel restricted, and economic development halted. Leveraging city-level mobility and case data across mainland China, our analysis shows that the spatial dissemination of COVID-19 in mainland China can be well explained by the human migration from Wuhan and there will be very different outcomes if the COVID-19 outbreak occurred in other cities. For example, the outbreak in Beijing or Guangzhou would result in a $\sim$90% increase of COVID-19 cases at the end of the Chinese New Year holiday. After the implementation of a series of control measures, human mobility had experienced substantial changes toward containing the spread of COVID-19. Our results also suggest an inequality of economic deprivation as less developed areas generally suffered more severe economic recession during the COVID-19. Intuitively, it's anticipated that cities with more confirmed cases would suffer more economic losses. However, for cities outside of Hubei province, we don't observe such a phenomenon. Our work has important implications for the mitigation of disease and the reevaluation of the social and economic consequences of COVID-19 on our society.