The outbreak of COVID-19 in March 2020 led to a shutdown of economic activities in Europe. This included the sports sector, since public gatherings were prohibited. The German Bundesliga was among the first sport leagues realising a restart without spectators. Several recent studies suggest that the home advantage of teams was eroded for the remaining matches. Our paper analyses the reaction by bookmakers to the disappearance of such home advantage. We show that bookmakers had problems to adjust the betting odds in accordance to the disappeared home advantage, opening opportunities for profitable betting strategies.

Miles et al. [1] recently produced an analysis of the costs and benefits of lockdown policies in the face of COVID-19, focussing on the case of the U.K. They argue that the March-June UK lockdown was more costly than the benefit of lives saved, if the latter are evaluated using the NICE threshold of {\pounds}30000 for a quality-adjusted life year (QALY). Looking forwards, they argue that the costs of a lockdown for 13 weeks from mid-June would be vastly greater than the benefits under any plausible QALY costing, even in a scenario in which easing lockdown led to a second infection wave that caused more than 7000 deaths a week by mid-September. I note here two key problems that certainly significantly affect their estimates and cast doubt on their conclusions. Firstly, they cut off their calculations arbitrarily after 13 weeks, without costing the epidemic state at the end of the period. That is, they assume that we should be indifferent between mid-September states of 13 deaths a week and 7500 deaths a week, and corresponding infection rates. This seems indefensible unless one assumes that (a) there will be no future vaccine and no future improvements in treatment or in non-medical interventions, (b) that COVID-19 will inevitably continue to propagate until herd immunity is reached. Even under these assumptions it is very questionable. Secondly, they ignore the costs of serious illness, possible long-term lowering of life quality, and possible lowering of life expectancy for COVID-19 survivors. These are uncertain, but clearly not negligible, and plausibly comparable to or larger than the costs in lives lost.

Many countries embroiled in non-religious civil conflicts have experienced a dramatic increase in religious competition in recent years. This study examines whether increasing competition between religions affects violence in non-religious conflicts. The study focuses on Colombia, a deeply Catholic country that has suffered one of the world's longest-running internal conflicts and, in the last few decades, has witnessed an intense increase in religious competition between the Catholic Church and new non-Catholic churches. The estimation of a dynamic treatment effect model shows that establishing the first non-Catholic church in a municipality substantially increases the probability of an attack by a left-wing guerrilla group. Further analysis suggests that the increase in guerrilla attacks is associated with the expectation among guerrilla groups that their membership will decline as a consequence of more intense competition with religious groups for followers.

We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involves studying the interaction of our uncertainty with controls which determine the filtration. We also run a simple numerical example which illustrates the interaction between the willingness to explore and uncertainty aversion of the agent when making decisions.

In this paper, a refined Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for commodity markets. The refinement of the BN-S model is obtained with various machine and deep learning algorithms. The refinement leads to the extraction of a deterministic parameter from the empirical data set. The problem is transformed to an appropriate classification problem with a couple of different approaches: the volatility approach and the duration approach. The analysis is implemented to the Bakken crude oil data and the aforementioned deterministic parameter is obtained for a wide range of data sets. With the implementation of this parameter in the refined model, the resulting model performs much better than the classical BN-S model.

We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behaviour on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions.

This paper is part of a coordinated collection of papers on prime-age male earnings volatility. Each paper produces a similar set of statistics for the same reference population using a different primary data source. Our primary data source is the Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) infrastructure files. Using LEHD data from 1998 to 2016, we create a well-defined population frame to facilitate accurate estimation of temporal changes comparable to designed longitudinal samples of people. We show that earnings volatility, excluding increases during recessions, has declined over the analysis period, a finding robust to various sensitivity analyses. Although we find volatility is declining, the effect is not homogeneous, particularly for workers with tenuous labor force attachment for whom volatility is increasing. These "not stable" workers have earnings volatility approximately 30 times larger than stable workers, but more important for earnings volatility trends we observe a large increase in the share of stable employment from 60% in 1998 to 67% in 2016, which we show to largely be responsible for the decline in overall earnings volatility. To further emphasize the importance of not stable and/or low earning workers we also conduct comparisons with the PSID and show how changes over time in the share of workers at the bottom tail of the cross-sectional earnings distributions can produce either declining or increasing earnings volatility trends.

The latent order book of Donier et al. is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.

We present multigrid iterative algorithms for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithms are based on our recent developed compact finite difference scheme coupled with Hermite interpolation for solving the m coupled partial differential equations consisting of the asset, delta, gamma, and speed options. In the algorithms, we first use the Gauss-Seidel as a smoother, and then implement V-cycle and modified multigrid strategies for solving our discretized equations. Hermite interpolation with Newton interpolatory divided difference (as the basis) is used in estimating the coupled asset, delta, gamma, and speed options in the set of equations. A numerical experiment is performed with the two-regimes example and compared with other existing methods to validate the optimal strategy. Results show that these algorithms provide fast and efficient tools for pricing American put options with regime-switching.

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets where we consider traders with information on the stock price direction and stock return mean. The Black-Scholes-Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

In this paper, I empirically investigate how the openness of political institutions to diverse representation can impact conflict-related violence. By exploiting plausibly exogenous variations in the number of councillors in Colombian municipalities, I develop two sets of results. First, regression discontinuity estimates show that larger municipal councils have a considerably greater number of political parties with at least one elected representative. I interpret this result as evidence that larger municipal councils are more open to diverse political participation. The estimates also reveal that non-traditional parties are the main beneficiaries of this greater political openness. Second, regression discontinuity estimates show that political openness substantially decreases conflict-related violence, namely the killing of civilian non-combatants. By exploiting plausibly exogenous variations in local election results, I show that the lower level of political violence stems from greater participation by parties with close links to armed groups. Using data about the types of violence employed by these groups, and representation at higher levels of government, I argue that armed violence has decreased not because of power-sharing arrangements involving armed groups linked to the parties with more political representation, but rather because armed groups with less political power and visibility are deterred from initiating certain types of violence.

In this paper, we propose a 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 asymmetry, that have been empirically observed for asset return distributions. On the new market model, we discuss a new portfolio optimization method, which is an extension of Markowitz's mean-variance optimization. The new optimization method considers not only reward and dispersion but also asymmetry. The efficient frontier is also extended to a curved surface on three-dimensional space of reward, dispersion, and asymmetry. We also propose a new performance measure which is an extension of the 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 under the model. Based on the empirical evidence presented in this paper, our framework offers realistic portfolio optimization and tractable methods for portfolio risk management.

We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies are compared to classical stochastic control techniques on several payoffs using a variance criterion. One of the proposed algorithm is flexible enough to be used with several existing risk criteria. We furthermore propose a new moment-based risk criteria.

We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz function. In addition, we show that Haezendonck-Goovaerts principles satisfy the stronger Lebesgue property if and only if the reference Orlicz function fulfills the so-called $\Delta_2$ condition. We also discuss (semi)continuity properties with respect to $\Phi$-weak convergence of probability measures. In particular, we show that Haezendonck-Goovaerts principles, restricted to the corresponding Young class, are always lower semicontinuous with respect to the $\Phi$-weak convergence.

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a return series. The realized EGARCH model is extended by adopting a standardized Student-t and a standardized skewed Student-t distribution for the return equation. Different types of realized measures, such as sub-sampled realized variance, sub-sampled realized range, and realized kernel, are considered in the paper. The Bayesian Markov chain Monte Carlo (MCMC) estimation employs the robust adaptive Metropolis algorithm (RAM) in the burn in period and the standard random walk Metropolis in the sample period. The Bayesian estimators show more favourable results than maximum likelihood estimators in a simulation study. We test the proposed models with several indices to forecast one-step-ahead Value at Risk (VaR) and Expected Shortfall (ES) over a period of 1000 days. Rigorous tail risk forecast evaluations show that the realized EGARCH models employing the standardized skewed Student-t distribution and incorporating sub-sampled realized range are favored, compared to a range of models.