Results of a convincing causal statistical inference related to socio-economic phenomena are treated as especially desired background for conducting various socio-economic programs or government interventions. Unfortunately, quite often real socio-economic issues do not fulfill restrictive assumptions of procedures of causal analysis proposed in the literature. This paper indicates certain empirical challenges and conceptual opportunities related to applications of procedures of data depth concept into a process of causal inference as to socio-economic phenomena. We show, how to apply a statistical functional depths in order to indicate factual and counterfactual distributions commonly used within procedures of causal inference. The presented framework is especially useful in a context of conducting causal inference basing on official statistics, i.e., basing on already existing databases. Methodological considerations related to extremal depth, modified band depth, Fraiman-Muniz depth, and multivariate Wilcoxon sum rank statistic are illustrated by means of example related to a study of an impact of EU direct agricultural subsidies on a digital development in Poland in a period of 2012-2019.

We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical methodology to financial uninterrupted daily trends returns and to other derived observable. In our opinion, to study distributional symmetry, trends returns offer more advantages than the commonly used daily financial returns; the two most important being: 1) Trends returns involve sampling over different time scales and 2) By construction, this variable time series contains practically the same number of non-negative and negative entry values. We also show that these time multi-scale returns display distributional bi-modality. Daily financial indices analyzed in this work, are the Mexican IPC, the American DJIA, DAX from Germany and the Japanese Market index Nikkei, covering a time period from 11-08-1991 to 06-30-2017. We show that, at the time scale resolution and significance considered in this paper, it is almost always feasible to find an interval of possible symmetry points containing one most plausible symmetry point denoted by C. Finally, we study the temporal evolution of C showing that this point is seldom zero and responds with sensitivity to extreme market events.

This paper analyzes a class of MFGs with singular controls motivated from the partially reversible problem. It establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation, and presents sensitivity analysis to compare the single-player game with the MFG. Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine game effects even without heterogeneity among players and additional common noise.

In this work we use Recurrent Neural Networks and Multilayer Perceptrons to predict NYSE, NASDAQ and AMEX stock prices from historical data. We experiment with different architectures and compare data normalization techniques. Then, we leverage those findings to question the efficient-market hypothesis through a formal statistical test.

Monte Carlo methods are critical to many routines in quantitative finance such as derivatives pricing, hedging and risk metrics. Unfortunately, Monte Carlo methods are very computationally expensive when it comes to running simulations in high-dimensional state spaces where they are still a method of choice in the financial industry. Recently, Tensor Processing Units (TPUs) have provided considerable speedups and decreased the cost of running Stochastic Gradient Descent (SGD) in Deep Learning. After highlighting computational similarities between training neural networks with SGD and simulating stochastic processes, we ask in the present paper whether TPUs are accurate, fast and simple enough to use for financial Monte Carlo. Through a theoretical reminder of the key properties of such methods and thorough empirical experiments we examine the fitness of TPUs for option pricing, hedging and risk metrics computation. In particular we demonstrate that, in spite of the use of mixed precision, TPUs still provide accurate estimators which are fast to compute when compared to GPUs. We also show that the Tensorflow programming model for TPUs is elegant, expressive and simplifies automated differentiation.