This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation setting, based on a theoretical hedging framework discussed in existing literature. We look at hedging CVA market risk for a portfolio with European options on a stock, first in a Black-Scholes setting, then in a Merton jump-diffusion setting. Furthermore, we analyze the trading business at a bank after including xVAs in pricing. We provide insights into the hedging of derivatives and their xVAs by analyzing and visualizing the cash-flows of a portfolio from a desk structure perspective. The case study shows that not charging CVA at trade inception results in an expected loss. Furthermore, hedging CVA market risk is crucial to end up with a stable trading strategy. In the Black-Scholes setting this can be done using the underlying stock, whereas in the Merton jump-diffusion setting we need to add extra options to the hedge portfolio to properly hedge the jump risk. In addition to the simulation, we derive analytical results that explain our observations from the numerical experiments. Understanding the hedging of CVA helps to deal with xVAs in a practical setting.

The development of Digital Economy sets its own requirements for the formation and development of so-called digital doubles and digital shadows of real objects (subjects/regions). An integral element of their development and application is a multi-level matrix of targets and resource constraints (time, financial, technological, production, etc.). The volume of statistical information collected for a digital double must meet several criteria: be objective, characterize the real state of the managed object as accurately as possible, contain all the necessary information on all managed parameters, and at the same time avoid unnecessary and duplicate indicators ("information garbage"). The relevance of forming the profile of the "digital shadow of the region" in the context of multitasking and conflict of departmental and Federal statistics predetermined the goal of the work-to form a system of indicators of the socio-economic situation of regions based on the harmonization of information resources. In this study, an inventory of the composition of indicators of statistical forms for their relevance and relevance was carried out on the example of assessing the economic health of the subject and the level of provision of banking services

Cryptocurrency history begins in 2008 as a means of payment proposal. However, cryptocurrencies evolved into complex, high yield speculative assets. Contrary to traditional financial instruments, they are not (mostly) traded in organized, law-abiding venues, but on online platforms, where anonymity reigns. This paper examines the long term memory in return and volatility, using high frequency time series of eleven important coins. Our study covers the pre-Covid-19 and the subsequent pandemia period. We use a recently developed method, based on the wavelet transform, which provides more robust estimators of the Hurst exponent. We detect that, during the peak of Covid-19 pandemic (around March 2020), the long memory of returns was only mildly affected. However, volatility suffered a temporary impact in its long range correlation structure. Our results could be of interest for both academics and practitioners.

We present a model for the equilibrium frequency of offenses and the informativeness of witness reports when potential offenders can commit multiple offenses and witnesses are subject to retaliation risk and idiosyncratic reporting preferences. We compare two ways of handling multiple accusations discussed in legal scholarship: (i) When convictions are based on the probability that the defendant committed at least one, unspecified offense and entail a severe punishment, potential offenders induce negative correlation in witnesses' private information, which leads to uninformative reports, information aggregation failures, and frequent offenses in equilibrium. Moreover, lowering the punishment in case of conviction can improve deterrence and the informativeness of witnesses' reports. (ii) When accusations are treated separately to adjudicate guilt and conviction entails a severe punishment, witness reports are highly informative and offenses are infrequent in equilibrium.

We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with ambiguity. We obtain the dynamic consistency of indifference pricing with ambiguity preferences. Finally, we obtain comparative statics.

During the past few decades, globalization and protectionism have ebbed and flowed from time to time among economies. The movements demand formal analytics that can help countries make better trade policies. They also imply that the best trade policies could be time-varying and country-specific. Economies and their imports and exports constitute a counterbalanced network where conflict and cooperation are two sides of the same coin. A country could improve its relative strength in the network by embracing globalization, protectionism, or trade wars. This paper provides necessary conditions for globalization and trade wars, evaluates their side effects, identifies the right targets for conflict or collaboration, and recommends fair resolutions for trade wars. Data and events from the past twenty years support these conditions.

Up-to-date poverty maps are an important tool for policymakers, but until now, have been prohibitively expensive to produce. We propose a generalizable prediction methodology to produce poverty maps at the village level using geospatial data and machine learning algorithms. We tested the proposed method for 25 Sub-Saharan African countries and validated them against survey data. The proposed method can increase the validity of both single country and cross-country estimations leading to higher precision in poverty maps of the 25 countries than previously available. More importantly, our cross-country estimation enables the creation of poverty maps when it is not practical or cost-effective to field new national household surveys, as is the case with many Sub-Saharan African countries and other low- and middle-income countries.

Trading a financial instrument induces a price response on itself and on other correlated instruments, a phenomenon known as cross-impact. Unfortunately, empirical measures of cross-impact are affected by a large estimation error due to both the large number of interactions to infer and the strongly fluctuating nature of price returns. In this study we propose a principled approach that leverages simple consistency criteria (symmetries, no-arbitrage conditions, correlation and liquidity limit-case properties) in order to impose ex-ante properties that might be required for practical applications. We validate our approach on empirical data for several asset classes, thus determining which properties are desirable across multiple markets. In particular, our results show that two cross-impact models perform well in all markets studied but only one is suitable for other applications, such as optimal execution.

We present a baseline stochastic framework for assessing inter-sectorial relationships in a generic economy. We show that - irrespective of the specific features of the technology matrix for a given country or a particular year - the Leontief multipliers (and any upstreamness/downstreamness indicator computed from the Leontief inverse matrix) follow a universal pattern, which we characterize analytically. We formulate a universal benchmark to assess the structural inter-dependence of sectors in a generic economy. Several empirical results on World Input-Output Database (WIOD, 2013 Release) are presented that corroborate our findings.

Temporal data are ubiquitous in the financial services (FS) industry -- traditional data like economic indicators, operational data such as bank account transactions, and modern data sources like website clickstreams -- all of these occur as a time-indexed sequence. But machine learning efforts in FS often fail to account for the temporal richness of these data, even in cases where domain knowledge suggests that the precise temporal patterns between events should contain valuable information. At best, such data are often treated as uniform time series, where there is a sequence but no sense of exact timing. At worst, rough aggregate features are computed over a pre-selected window so that static sample-based approaches can be applied (e.g. number of open lines of credit in the previous year or maximum credit utilization over the previous month). Such approaches are at odds with the deep learning paradigm which advocates for building models that act directly on raw or lightly processed data and for leveraging modern optimization techniques to discover optimal feature transformations en route to solving the modeling task at hand. Furthermore, a full picture of the entity being modeled (customer, company, etc.) might only be attainable by examining multiple data streams that unfold across potentially vastly different time scales. In this paper, we examine the different types of temporal data found in common FS use cases, review the current machine learning approaches in this area, and finally assess challenges and opportunities for researchers working at the intersection of machine learning for temporal data and applications in FS.

Optimal order execution is widely studied by industry practitioners and academic researchers because it determines the profitability of investment decisions and high-level trading strategies, particularly those involving large volumes of orders. However, complex and unknown market dynamics pose significant challenges for the development and validation of optimal execution strategies. In this paper, we propose a model-free approach by training Reinforcement Learning (RL) agents in a realistic market simulation environment with multiple agents. First, we configure a multi-agent historical order book simulation environment for execution tasks built on an Agent-Based Interactive Discrete Event Simulation (ABIDES) [arXiv:1904.12066]. Second, we formulate the problem of optimal execution in an RL setting where an intelligent agent can make order execution and placement decisions based on market microstructure trading signals in High Frequency Trading (HFT). Third, we develop and train an RL execution agent using the Double Deep Q-Learning (DDQL) algorithm in the ABIDES environment. In some scenarios, our RL agent converges towards a Time-Weighted Average Price (TWAP) strategy. Finally, we evaluate the simulation with our RL agent by comparing it with a market replay simulation using real market Limit Order Book (LOB) data.

The topics treated in this thesis are inherently two-fold. The first part considers the problem of a market maker optimally setting bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. This stochastic control problem under partial information is solved by means of stochastic filtering, control and PDMPs theory. The value function is characterized as the unique continuous viscosity solution of its dynamic programming equation and numerically compared with its full information counterpart. The optimal full information spreads are shown to be biased when the exact market regime is unknown, as the market maker needs to adjust for additional regime uncertainty in terms of PnL sensitivity and observable order flow volatility.

The second part deals with numerically solving nonzero-sum stochastic impulse control games. These offer a realistic and far-reaching modelling framework, but the difficulty in solving such problems has hindered their proliferation. A policy-iteration-type solver is proposed to solve an underlying system of quasi-variational inequalities, and it is validated numerically with reassuring results.

Eventually, the focus is put on games with a symmetric structure and an improved algorithm is put forward. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. The algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of the currently available theory.

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path dependent partial differential equations (PPDEs). Moreover, we provide a dimension reduction result based on the new notion of "semifiltrations", which identifies appropriate Markovian state variables based on the constraints and the cost function. Our technique is then applied to the exact calibration of volatility models to the prices of general path dependent derivatives.

We develop a framework for price-mediated contagion in financial systems where banks are forced to liquidate assets to satisfy a risk-weight based capital adequacy requirement. In constructing this modeling framework, we introduce a two-tier pricing structure: the volume weighted average price that is obtained by any bank liquidating assets and the terminal mark-to-market price used to account for all assets held at the end of the clearing process. We consider the case of multiple illiquid assets and develop conditions for the existence and uniqueness of clearing prices. We provide a closed-form representation for the sensitivity of these clearing prices to the system parameters, and use this result to quantify: (1) the cost of regulation, in stress scenarios, faced by the system as a whole and the individual banks, and (2) the value of providing bailouts to consider when such notions are financially advisable. Numerical case studies are provided to study the application of this model to data.

Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensions of scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions, which evaluate the risk dynamics on the selectors of acceptable capital allocations; or (2) set-valued backward stochastic differential equations, which evaluate the risk dynamics on the full set of acceptable capital allocations as a singular object. In this work, the discrete time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures in continuous time.

Copulas are becoming an essential tool in analyzing data and knowing local copula bounds with a fixed value of a given measure of association is turning into a prerequisite in the early stage of exploratory data analysis. These bounds have been computed for Spearman's rho, Kendall's tau, and Blomqvist's beta. The importance of another two measures of association, Spearman's footrule and Gini's gamma, has been reconfirmed recently. It is the main purpose of this paper to fill in the gap and present the mentioned local bounds for these two measures as well. It turns out that this is a quite non-trivial endeavor as the bounds are quasi-copulas that are not copulas for certain values of the two measures. We also give relations between these two measures of association and Blomqvist's beta.

Stablecoins are one of the most widely capitalized type of cryptocurrency. However, their risks vary significantly according to their design and are often poorly understood. We seek to provide a sound foundation for stablecoin theory, with a risk-based functional characterization of the economic structure of stablecoins. First, we match existing economic models to the disparate set of custodial systems. Next, we characterize the unique risks that emerge in non-custodial stablecoins and develop a model framework that unifies existing models from economics and computer science. We further discuss how this modeling framework is applicable to a wide array of cryptoeconomic systems, including cross-chain protocols, collateralized lending, and decentralized exchanges. These unique risks yield unanswered research questions that will form the crux of research in decentralized finance going forward.

Thanks to the increasing availability of granular, yet high-dimensional, firm level data, machine learning (ML) algorithms have been successfully applied to address multiple research questions related to firm dynamics. Especially supervised learning (SL), the branch of ML dealing with the prediction of labelled outcomes, has been used to better predict firms' performance. In this contribution, we will illustrate a series of SL approaches to be used for prediction tasks, relevant at different stages of the company life cycle. The stages we will focus on are (i) startup and innovation, (ii) growth and performance of companies, and (iii) firms exit from the market. First, we review SL implementations to predict successful startups and R&D projects. Next, we describe how SL tools can be used to analyze company growth and performance. Finally, we review SL applications to better forecast financial distress and company failure. In the concluding Section, we extend the discussion of SL methods in the light of targeted policies, result interpretability, and causality.

We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these SC points, we can perform Monte Carlo simulations with large time steps. Error analysis confirms that this data-driven scheme results in accurate SDE solutions in the sense of strong convergence, provided the learning methodology is robust and accurate. With a variant method called the compression-decompression collocation and interpolation technique, we can drastically reduce the number of neural network functions that have to be learned, so that computational speed is enhanced. Numerical results show the high quality strong convergence error results, when using large time steps, and the novel scheme outperforms some classical numerical SDE discretizations. Some applications, here in financial option valuation, are also presented.