Research articles for the 2020-08-02

Epidemic response to physical distancing policies and their impact on the outbreak risk
Fabio Vanni,David Lambert,Luigi Palatella

We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of 'lockdown' to reduce the number of new infections. Specifically we use a collisional approach to an infection-age structured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical proximity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distancing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interactions among people, which may help policy makers to improve remote-working organizational structure.

Improving the Scalability of a Prosumer Cooperative Game with K-Means Clustering
Liyang Han,Thomas Morstyn,Constance Crozier,Malcolm McCulloch

Among the various market structures under peer-to-peer energy sharing, one model based on cooperative game theory provides clear incentives for prosumers to collaboratively schedule their energy resources. The computational complexity of this model, however, increases exponentially with the number of participants. To address this issue, this paper proposes the application of K-means clustering to the energy profiles following the grand coalition optimization. The cooperative model is run with the "clustered players" to compute their payoff allocations, which are then further distributed among the prosumers within each cluster. Case studies show that the proposed method can significantly improve the scalability of the cooperative scheme while maintaining a high level of financial incentives for the prosumers.

Infinite-horizon risk-averse optimal switching under partial information and related systems of reflected backward stochastic difference equations
Randall Martyr,John Moriarty,Magnus Perninge

We obtain structural results for non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example illustrates the interaction between partial information and risk aversion in the special case of optimal stopping problems.

Investment sizing with deep learning prediction uncertainties for high-frequency Eurodollar futures trading
Trent Spears,Stefan Zohren,Stephen Roberts

In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important because it permits the scaling of investment size across trade opportunities in a principled and data-driven way. We showcase this insight with a prediction model and find clear outperformance based on a Sharpe ratio metric, relative to trading strategies that either do not take uncertainty into account, or that utilize an alternative market-based statistic as a proxy for uncertainty. Of added novelty is our modelling of high-frequency data at the top level of the Eurodollar Futures limit order book for each trading day of 2018, whereby we predict interest rate curve changes on small time horizons. We are motivated to study the market for these popularly-traded interest rate derivatives since it is deep and liquid, and contributes to the efficient functioning of global finance -- though there is relatively little by way of its modelling contained in the academic literature. Hence, we verify the utility of prediction models and uncertainty estimates for trading applications in this complex and multi-dimensional asset price space.

Job market effects of COVID-19 on urban Ukrainian households
Tymofii Brik,Maksym Obrizan

The employment status of billions of people has been affected by the COVID epidemic around the Globe. New evidence is needed on how to mitigate the job market crisis, but there exists only a handful of studies mostly focusing on developed countries. We fill in this gap in the literature by using novel data from Ukraine, a transition country in Eastern Europe, which enacted strict quarantine policies early on. We model four binary outcomes to identify respondents (i) who are not working during quarantine, (ii) those who are more likely to work from home, (iii) respondents who are afraid of losing a job, and, finally, (iv) survey participants who have savings for 1 month or less if quarantine is further extended. Our findings suggest that respondents employed in public administration, programming and IT, as well as highly qualified specialists, were more likely to secure their jobs during the quarantine. Females, better educated respondents, and those who lived in Kyiv were more likely to work remotely. Working in the public sector also made people more confident about their future employment perspectives. Although our findings are limited to urban households only, they provide important early evidence on the correlates of job market outcomes, expectations, and financial security, indicating potential deterioration of socio-economic inequalities.

On Single Point Forecasts for Fat-Tailed Variables
Nassim Nicholas Taleb,Yaneer Bar-Yam,Pasquale Cirillo

We discuss common errors and fallacies when using naive "evidence based" empiricism and point forecasts for fat-tailed variables, as well as the insufficiency of using naive first-order scientific methods for tail risk management. We use the COVID-19 pandemic as the background for the discussion and as an example of a phenomenon characterized by a multiplicative nature, and what mitigating policies must result from the statistical properties and associated risks. In doing so, we also respond to the points raised by Ioannidis et al. (2020).

Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
Young Shin Kim

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution is able to capture two stylized facts: fat-tails and asymmetric tails, that have been empirically observed for asset return distributions. On the new market model, a new portfolio optimization method, which is an extension of Markowitz's mean-variance optimization, is discussed. The new optimization method considers not only reward and dispersion but also asymmetry. The efficient frontier is also extended from the mean-variance curve to a surface on three dimensional space of reward, dispersion, and asymmetry. We also propose a new performance measure which is an extension of Sharpe Ratio. Moreover, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal Value-at-Risk (VaR) and the marginal Conditional VaR (CVaR). We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average. First perform the new portfolio optimization and then demonstrating how the marginal VaR and marginal CVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers realistic portfolio optimization and tractable methods for portfolio risk management.

The Hansen ratio in mean--variance portfolio theory
Aleš Černý

It is shown that the ratio between the mean and the $L^2$-norm leads to a particularly parsimonious description of the mean-variance efficient frontier and the dual pricing kernel restrictions known as the Hansen-Jagannathan (HJ) bounds. Because this ratio has not appeared in economic theory previously, it seems appropriate to name it the Hansen ratio. The initial treatment of the mean-variance theory via the Hansen ratio is extended in two directions, to monotone mean-variance preferences and to arbitrary Hilbert space setting. A multiperiod example with IID returns is also discussed.