Distress propagation occurs in connected networks, its rate and extent being dependent on network topology. To study this, we choose economic production networks as a paradigm. An economic network can be examined at many levels: linkages among individual agents (microscopic), among firms/sectors (mesoscopic) or among countries (macroscopic). New emergent dynamical properties appear at every level, so the granularity matters. For viral epidemics, even an individual node may act as an epicenter of distress and potentially affect the entire network. Economic networks, however, are known to be immune at the micro-levels and more prone to failure in the meso/macro-levels. We propose a dynamical interaction model to characterize the mechanism of distress propagation, across different modules of a network, initiated at different epicenters. Vulnerable modules often lead to large degrees of destabilization. We demonstrate our methodology using a unique empirical data-set of input-output linkages across 0.14 million firms in one administrative state of India, a developing economy. The network has multiple hub-and-spoke structures that exhibits moderate disassortativity, which varies with the level of coarse-graining. The novelty lies in characterizing the production network at different levels of granularity or modularity, and finding `too-big-to-fail' modules supersede `too-central-to-fail' modules in distress propagation.

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.

A perspective is taken on the intangible complexity of economic and social systems by investigating the underlying dynamical processes that produce, store and transmit information in financial time series in terms of the \textit{moving average cluster entropy}. An extensive analysis has evidenced market and horizon dependence of the \textit{moving average cluster entropy} in real world financial assets. The origin of the behavior is scrutinized by applying the \textit{moving average cluster entropy} approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). To that end, an extensive set of series is generated with a broad range of values of the Hurst exponent $H$ and of the autoregressive, differencing and moving average parameters $p,d,q$. A systematic relation between \textit{moving average cluster entropy}, \textit{Market Dynamic Index} and long-range correlation parameters $H$, $d$ is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter $ d\simeq 0.05$, $d\simeq 0.15$ and $ d\simeq 0.25$ are consistent with \textit{moving average cluster entropy} results obtained in time series of DJIA, S\&P500 and NASDAQ.

We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the participation matrix based on superposition of Gaussian functions is proposed and we show that small eigenvalues correspond to localized states. Nonetheless, some level of localization is also present for bigger eigenvalues probably caused by the fat tails of the distribution of returns of these assets. We also show through a clustering study that the digital currencies tend to stagger together. We conclude the paper showing that this correlation structure leads to an Epps effect.

We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised kernels. We apply these results to the rough Heston model, with square-root diffusion coefficient, recently proposed in Mathematical Finance to model the volatility of asset prices.

We present a natural extension of the SABR model to price both backward and forward-looking RFR caplets in a post-Libor world. Forward-looking RFR caplets can be priced using the market standard approximations of Hagan et al. (2002). We provide closed-form effective SABR parameters for pricing backward-looking RFR caplets. These results are useful for smile interpolation and for analyzing backward and forward-looking smiles in normalized units.

We study search, evaluation, and selection of candidates of unknown quality for a position. We examine the effects of "soft" affirmative action policies increasing the relative percentage of minority candidates in the candidate pool. We show that, while meant to encourage minority hiring, such policies may backfire if the evaluation of minority candidates is noisier than that of non-minorities. This may occur even if minorities are at least as qualified and as valuable as non-minorities. The results provide a possible explanation for why certain soft affirmative action policies have proved counterproductive, even in the absence of (implicit) biases.

We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth. Based on the work [9] with an additional stochastic payoff function, we characterize the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equation (BSDE for short) with unbounded terminal condition. In regard to discrete problem, we get the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provide some useful prior estimates about the solutions with the help of auxiliary forward-backward SDE system and Malliavin calculus. Finally, we obtain the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.