When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their aggregative efficiency index. Networks where agents observe multiple neighbors but not their common predecessors confound information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial differential equations with a fixed domain by using logarithm transformation and taking additional derivatives. With the addition of an intermediate function with a fixed free boundary, a quadratic formula is derived to compute the velocity of the optimal exercise boundary analytically. Furthermore, we implement an extrapolation method to ensure that at least, a third-order accuracy in space is maintained at the boundary point when computing the optimal exercise boundary from its derivative. As such, it enables us to employ fourth-order spatial and temporal discretization with Dirichlet boundary conditions for obtaining the numerical solution of the asset option, option Greeks, and the optimal exercise boundary. The advantage of the Runge-Kutta-Fehlberg method is based on error control and the adjustment of the time step to maintain the error at a certain threshold. By comparing with some existing methods in the numerical experiment, it shows that the present method has a better performance in terms of computational speed and provides a more accurate solution.

This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation conditional on an event of zero probability to a ratio involving conditional expectations whose conditioning events have stricktly positive probability. We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show that the estimator using this novel representation outperforms the standard Monte Carlo estimator in terms of bias and variance. Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters.

We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time. We allow for trading in both directions and for c\`adl\`ag semimartingales as execution strategies. We derive a quadratic BSDE that under appropriate assumptions characterizes minimal execution costs and identify conditions under which an optimal execution strategy exists. We also investigate qualitative aspects of optimal strategies such as, e.g., appearance of strategies with infinite variation or existence of block trades and discuss connections with the discrete-time formulation of the problem. Our findings are illustrated in several examples.

We investigate the allegation that legacy U.S. airlines communicated via earnings calls to coordinate with other legacy airlines in offering fewer seats on competitive routes. To this end, we first use text analytics to build a novel dataset on communication among airlines about their capacity choices. Estimates from our preferred specification show that the number of offered seats is 2% lower when all legacy airlines in a market discuss the concept of "capacity discipline." We verify that this reduction materializes only when legacy airlines communicate concurrently, and that it cannot be explained by other possibilities, including that airlines are simply announcing to investors their unilateral plans to reduce capacity, and then following through on those announcements.

We use deep neural networks to estimate an asset pricing model for individual stock returns that takes advantage of the vast amount of conditioning information, while keeping a fully flexible form and accounting for time-variation. The key innovations are to use the fundamental no-arbitrage condition as criterion function, to construct the most informative test assets with an adversarial approach and to extract the states of the economy from many macroeconomic time series. Our asset pricing model outperforms out-of-sample all benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors and identifies the key factors that drive asset prices.

The COVID-19 pandemic has been influencing travel behaviour in many urban areas around the world since the beginning of 2020. As a consequence, bike-sharing schemes have been affected partly due to the change in travel demand and behaviour as well as a shift from public transit. This study estimates the varying effect of the COVID-19 pandemic on the London bike-sharing system (Santander Cycles) over the period March-December 2020. We employed a Bayesian second-order random walk time-series model to account for temporal correlation in the data. We compared the observed number of cycle hires and hire time with their respective counterfactuals (what would have been if the pandemic had not happened) to estimate the magnitude of the change caused by the pandemic. The results indicated that following a reduction in cycle hires in March and April 2020, the demand rebounded from May 2020, remaining in the expected range of what would have been if the pandemic had not occurred. This could indicate the resiliency of Santander Cycles. With respect to hire time, an important increase occurred in April, May, and June 2020, indicating that bikes were hired for longer trips, perhaps partly due to a shift from public transit.

In this research work, an explicit Runge-Kutta-Fehlberg (RKF) time integration with a fourth-order compact finite difference scheme in space and a high order analytical approximation of the optimal exercise boundary is employed for solving the regime-switching pricing model. In detail, we recast the free boundary problem into a system of nonlinear partial differential equations with a multi-fixed domain. We then introduce a transformation based on the square root function with a Lipschitz character from which a high order analytical approximation is obtained to compute the derivative of the optimal exercise boundary in each regime. We further compute the boundary values, asset option, and the option Greeks for each regime using fourth-order spatial discretization and adaptive time integration. In particular, the coupled assets options and option Greeks are estimated using Hermite interpolation with Newton basis. Finally, a numerical experiment is carried out with two- and four-regimes examples and results are compared with the existing methods. The results obtained from the numerical experiment show that the present method provides better performance in terms of computational speed and more accurate solutions with a large step size.

We carry out a detailed large-scale data analysis of price response functions in the spot foreign exchange market for different years and different time scales. Such response functions provide quantitative information on the deviation from Markovian behavior. The price response functions show an increase to a maximum followed by a slow decrease as the time lag grows, in trade time scale and in physical time scale, for all analyzed years. Furthermore, we use a price increment point (pip) bid-ask spread definition to group different foreign exchange pairs and analyze the impact of the spread in the price response functions. We find that large pip spreads have a stronger impact on the response. This is similar to what has been found in stock markets.

The quarterly financial statement, or Form 10-Q, is one of the most frequently required filings for US public companies to disclose financial and other important business information. Due to the massive volume of 10-Q filings and the enormous variations in the reporting format, it has been a long-standing challenge to retrieve item-specific information from 10-Q filings that lack machine-readable hierarchy. This paper presents a solution for itemizing 10-Q files by complementing a rule-based algorithm with a Convolutional Neural Network (CNN) image classifier. This solution demonstrates a pipeline that can be generalized to a rapid data retrieval solution among a large volume of textual data using only typographic items. The extracted textual data can be used as unlabeled content-specific data to train transformer models (e.g., BERT) or fit into various field-focus natural language processing (NLP) applications.

Men and women systematically differ in their beliefs about their performance relative to others; in particular, men tend to be more overconfident. This paper provides support for one explanation for gender differences in overconfidence, performance-motivated reasoning, in which people distort how they process new information in ways that make them believe they outperformed others. Using a large online experiment, I find that male subjects distort information processing in ways that favor their performance, while female subjects do not systematically distort information processing in either direction. These statistically-significant gender differences in performance-motivated reasoning mimic gender differences in overconfidence; beliefs of male subjects are systematically overconfident, while beliefs of female subjects are well-calibrated on average. The experiment also includes political questions, and finds that politically-motivated reasoning is similar for both men and women. These results suggest that, while men and women are both susceptible to motivated reasoning in general, men find it particularly attractive to believe that they outperformed others.

We investigate and extend the results of Golts and Jones (2009) that an $\alpha$-weight angle resulting from unconstrained quadratic portfolio optimisations has an upper bound dependent on the condition number of the covariance matrix. This implies that better conditioned covariance matrices produce weights from unconstrained mean-variance optimisations that are better aligned with each assets expected return. We provide further clarity on the mathematical insights that relate the inequality between the $\alpha$-weight angle and the condition number and extend the result to include portfolio optimisations with gearing constraints. We provide an extended family of robust optimisations that include the gearing constraints, and discuss their interpretation.

Inferring the uncertainties in economic conditions are of significant importance for both decision makers as well as market players. In this paper, we propose a novel method based on Hidden Markov Model (HMM) to construct the Economic Condition Uncertainty (ECU) index that can be used to infer the economic condition uncertainties. The ECU index is a dimensionless index ranges between zero and one, this makes it to be comparable among sectors, regions and periods. We use the daily electricity consumption data of nearly 20 thousand firms in Shanghai from 2018 to 2020 to construct the ECU indexes. Results show that all ECU indexes, no matter at sectoral level or regional level, successfully captured the negative impacts of COVID-19 on Shanghai's economic conditions. Besides, the ECU indexes also presented the heterogeneities in different districts as well as in different sectors. This reflects the facts that changes in uncertainties of economic conditions are mainly related to regional economic structures and targeted regulation policies faced by sectors. The ECU index can also be easily extended to measure uncertainties of economic conditions in different fields which has great potentials in the future.

Most trading in cryptocurrency options is on inverse products, so called because the contract size is denominated in US dollars and they are margined and settled in crypto, typically bitcoin or ether. Their popularity stems from allowing professional traders in bitcoin or ether options to avoid transferring fiat currency to and from the exchanges. We derive new analytic pricing and hedging formulae for inverse options under the assumption that the underlying follows a geometric Brownian motion. The boundary conditions and hedge ratios exhibit relatively complex but very important new features which warrant further analysis and explanation. We also illustrate some inconsistencies, exhibited in time series of Deribit bitcoin option implied volatilities, which indicate that traders may be applying direct option hedging and valuation methods erroneously. This could be because they are unaware of the correct, inverse option characteristics which are derived in this paper.

We study one-shot Nash competition between an arbitrary number of identical dealers that compete for the order flow of a client. The client trades either because of proprietary information, exposure to idiosyncratic risk, or a mix of both trading motives. When quoting their price schedules, the dealers do not know the client's type but only its distribution, and in turn choose their price quotes to mitigate between adverse selection and inventory costs. Under essentially minimal conditions, we show that a unique symmetric Nash equilibrium exists and can be characterized by the solution of a nonlinear ODE.

We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink or deleverage a position for it to become acceptable. In particular, the Minkowski Deviation of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure. Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set, and the corresponding properties of the induced measure. Hence, we fill the gap that is the lack of an acceptance set for deviation measures. Dual characterizations in terms of polar sets and support functionals are provided.

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in describing the deviation between the nominal and actual distribution of the components of the index. In this scenario, we derive the optimal robust index tracking strategy in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented that allow us to compare the performance of this robust strategy with the optimal non-robust strategy. We show that, especially during market downturns, the robust strategy can be very advantageous.

We study a model in which before a conflict between two parties escalates into a war (in the form of an all-pay auction), a party can offer a take-it-or-leave-it bribe to the other one for a peaceful settlement. We distinguish between various degrees of peace prospects--implementability, weak security and strong security. We first characterize the necessary and sufficient conditions for peace implementability and weak security. We then show that weak security implies strong security. We also consider a requesting-a-bribe game and characterize the necessary and sufficient conditions for existence of a robust peaceful equilibrium. We find that all such robust peaceful equilibria share the same request.

This paper addresses reflected backward stochastic differential equations (RBSDE hereafter) that take the form of \begin{eqnarray*} \begin{cases} dY_t=f(t,Y_t, Z_t)d(t\wedge\tau)+Z_tdW_t^{\tau}+dM_t-dK_t,\quad Y_{\tau}=\xi,

Y\geq S\quad\mbox{on}\quad \Lbrack0,\tau\Lbrack,\quad \displaystyle\int_0^{\tau}(Y_{s-}-S_{s-})dK_s=0\quad P\mbox{-a.s..}\end{cases} \end{eqnarray*} Here $\tau$ is an arbitrary random time that might not be a stopping time for the filtration $\mathbb F$ generated by the Brownian motion $W$. We consider the filtration $\mathbb G$ resulting from the progressive enlargement of $\mathbb F$ with $\tau$ where this becomes a stopping time, and study the RBSDE under $\mathbb G$. Precisely, we focus on answering the following problems: a) What are the sufficient minimal conditions on the data $(f, \xi, S, \tau)$ that guarantee the existence of the solution of the $\mathbb G$-RBSDE in $L^p$ ($p>1$)? b) How can we estimate the solution in norm using the triplet-data $(f, \xi, S)$? c) Is there an RBSDE under $\mathbb F$ that is intimately related to the current one and how their solutions are related to each other? We prove that for any random time, having a positive Az\'ema supermartingale, there exists a positive discount factor ${\widetilde{\cal E}}$ that is vital in answering our questions without assuming any further assumption on $\tau$, and determining the space for the triplet-data $(f,\xi, S)$ and the space for the solution of the RBSDE as well.

The ongoing Rohingya refugee crisis is considered as one of the largest human-made humanitarian disasters of the 21st century. So far, Bangladesh is the largest recipient of these refugees. According to the United Nations Office for the Coordination of Humanitarian Affairs (UN OCHA), approximately 650,000 new entrants have been recorded since the new violence erupted on 25 August 2017 in the Rakhine state of Myanmar.1 However, such crisis is nothing new in Bangladesh, nor are the security-related challenges new that such an exodus brings with it. Ever since the military came to power in Myanmar (in 1962), Rohingya exodus to neighboring countries became a recurring incident. The latest mass exodus of Rohingyas from Rakhine state of Myanmar to Bangladesh is the largest of such influxes. Unlike, the previous refugee crisis, the ongoing crisis has wide-ranging security implications on Bangladesh. They are also varied and multifaceted. Thus, responsibilities for ensuring effective protection have become operationally multilateral. The problem of security regarding the Rohingya refugee issue is complicated by the Islamist insurgency, illicit methamphetamine/yaba drug trafficking, and HIV/AIDS/STI prevalence factors. The chapter examines the different dimensions of security challenges that the recent spell of Rohingya exodus brings to Bangladesh and the refugees themselves. In order to understand the challenges, firstly the chapter attempts to conceptualize the prominent security frameworks. Secondly, it examines the context and political economy behind the persecution of Rohingyas in the Rakhine state. Thirdly, it explores the political and military aspects of security. Fourthly, it explores the social and economic dimensions. Finally, it examines the environmental impacts of Rohingya crisis in Bangladesh.

Price movement forecasting aims at predicting the future trends of financial assets based on the current market conditions and other relevant information. Recently, machine learning(ML) methods have become increasingly popular and achieved promising results for price movement forecasting in both academia and industry. Most existing ML solutions formulate the forecasting problem as a classification(to predict the direction) or a regression(to predict the return) problem in the entire set of training data. However, due to the extremely low signal-to-noise ratio and stochastic nature of financial data, good trading opportunities are extremely scarce. As a result, without careful selection of potentially profitable samples, such ML methods are prone to capture the patterns of noises instead of real signals. To address the above issues, we propose a novel framework-LARA(Locality-Aware Attention and Adaptive Refined Labeling), which contains the following three components: 1)Locality-aware attention automatically extracts the potentially profitable samples by attending to their label information in order to construct a more accurate classifier on these selected samples. 2)Adaptive refined labeling further iteratively refines the labels, alleviating the noise of samples. 3)Equipped with metric learning techniques, Locality-aware attention enjoys task-specific distance metrics and distributes attention on potentially profitable samples in a more effective way. To validate our method, we conduct comprehensive experiments on three real-world financial markets: ETFs, the China's A-share stock market, and the cryptocurrency market. LARA achieves superior performance compared with the time-series analysis methods and a set of machine learning based competitors on the Qlib platform. Extensive ablation studies and experiments demonstrate that LARA indeed captures more reliable trading opportunities.