A group of heterogeneous players gathers information about an uncertain state before making decisions. Each player allocates his limited bandwidth between biased sources and the other players, and the resulting stochastic attention network facilitates the transmission of news from sources to him either directly or indirectly through the other players. The limit in the bandwidth leads the player to focus on his own-biased source, resulting in occasional cross-cutting exposures but most of the time a reinforcement of his predisposition. It also confines his attention to like-minded friends who, by attending to the same primary source as his, serve as secondary sources in case the news transmission from the primary source to him is disrupted. A mandate on impartial exposures to all biased sources disrupts echo chambers but entails ambiguous welfare consequences. Inside an echo chamber, even a small amount of heterogeneity between players can generate fat-tailed distributions of public opinion, and factors affecting the visibility of sources and players could have unintended consequences for public opinion and consumer welfare.

We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter, and it includes tilt and stretch parameters that control increment sizes. Option pricing formulas are written using q-binomial coefficients, and we study the convergence of this model to a Black-Scholes type formula in continuous time. A convergence rate of order O(1/N) is obtained when the tilt and stretch parameters are set equal to one.

Model-Free Reinforcement Learning has achieved meaningful results in stable environments but, to this day, it remains problematic in regime changing environments like financial markets. In contrast, model-based RL is able to capture some fundamental and dynamical concepts of the environment but suffer from cognitive bias. In this work, we propose to combine the best of the two techniques by selecting various model-based approaches thanks to Model-Free Deep Reinforcement Learning. Using not only past performance and volatility, we include additional contextual information such as macro and risk appetite signals to account for implicit regime changes. We also adapt traditional RL methods to real-life situations by considering only past data for the training sets. Hence, we cannot use future information in our training data set as implied by K-fold cross validation. Building on traditional statistical methods, we use the traditional "walk-forward analysis", which is defined by successive training and testing based on expanding periods, to assert the robustness of the resulting agent.

Finally, we present the concept of statistical difference's significance based on a two-tailed T-test, to highlight the ways in which our models differ from more traditional ones. Our experimental results show that our approach outperforms traditional financial baseline portfolio models such as the Markowitz model in almost all evaluation metrics commonly used in financial mathematics, namely net performance, Sharpe and Sortino ratios, maximum drawdown, maximum drawdown over volatility.

Backtesting risk measure forecasts requires identifiability (for model calibration and validation) and elicitability (for model comparison). We show that the three widely-used systemic risk measures conditional value-at-risk (CoVaR), conditional expected shortfall (CoES) and marginal expected shortfall (MES), which measure the risk of a position $Y$ given that a reference position $X$ is in distress, fail to be identifiable and elicitable on their own. As a remedy, we establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position $X$. While this resembles the situation of the classical risk measures expected shortfall (ES) and VaR concerning identifiability, a joint elicitability result fails. Therefore, we introduce a completely novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective scores. We introduce and investigate corresponding notions of multi-objective elicitability, which may prove beneficial in various applications beyond finance. In particular, we prove that conditional elicitability of two functionals implies joint multi-objective elicitability with respect to the lexicographic order on $\mathbb{R}^2$, which makes it applicable in the context of CoVaR, MES or (CoVaR, CoES), together with VaR. We describe corresponding comparative backtests of Diebold-Mariano type, for two-sided and 'one and a half'-sided hypotheses, which respect the particularities of the lexicographic order and which can be used in a regulatory setting. We demonstrate the viability of these backtesting approaches in simulations and in an empirical application to DAX 30 and S&P 500 returns.

The Internet of Value (IOV) with its distributed ledger technology (DLT) underpinning has created new forms of lending markets. As an integral part of the decentralised finance (DeFi) ecosystem, lending protocols are gaining tremendous traction, holding an aggregate liquidity supply of over $40 billion at the time of writing. In this paper, we enumerate the challenges of traditional money markets led by banks and lending platforms, and present advantageous characteristics of DeFi lending protocols that might help resolve deep-rooted issues in the conventional lending environment. With the examples of Maker, Compound and Aave, we describe in detail the mechanism of DeFi lending protocols. We discuss the persisting reliance of DeFi lending on the traditional financial system, and conclude with the outlook of the lending market in the IOV era.

We consider identification of peer effects under peer group miss-specification. Our model of group miss-specification allows for missing data and peer group uncertainty. Missing data can take the form of some individuals being completely absent from the data, and the researcher need not have any information on these individuals and may not even know that they are missing. We show that peer effects are nevertheless identifiable if these individuals are missing completely at random or missing at random, and propose a GMM estimator which jointly estimates the sampling probability and peer effects. In practice this means that the researcher need only have access to an individual/household level sample with group identifiers. The researcher may also be uncertain as to what is the relevant peer group for the outcome under study. We show that peer effects are nevertheless identifiable provided that the candidate peer groups are nested within one another (e.g. classroom, grade, school) and propose a non-linear least squares estimator. We conduct a Monte-Carlo experiment to demonstrate our identification results and the performance of the proposed estimators in a setting tailored to real data (the Dartmouth room-mate data).

This study leverages narrative from global newspapers to construct theme-based knowledge graphs about world events, demonstrating that features extracted from such graphs improve forecasts of industrial production in three large economies compared to a number of benchmarks. Our analysis relies on a filtering methodology that extracts "backbones" of statistically significant edges from large graph data sets. We find that changes in the eigenvector centrality of nodes in such backbones capture shifts in relative importance between different themes significantly better than graph similarity measures. We supplement our results with an interpretability analysis, showing that the theme categories "disease" and "economic" have the strongest predictive power during the time period that we consider. Our work serves as a blueprint for the construction of parsimonious - yet informative - theme-based knowledge graphs to monitor in real time the evolution of relevant phenomena in socio-economic systems.

In this paper, we provide causal evidence on abortions and risky health behaviors as determinants of mental health development among young women. Using administrative in- and outpatient records from Sweden, we apply a novel grouped fixed-effects estimator proposed by Bonhomme and Manresa (2015) to allow for time-varying unobserved heterogeneity. We show that the positive association obtained from standard estimators shrinks to zero once we control for grouped time-varying unobserved heterogeneity. We estimate the group-specific profiles of unobserved heterogeneity, which reflect differences in unobserved risk to be diagnosed with a mental health condition. We then analyze mental health development and risky health behaviors other than unwanted pregnancies across groups. Our results suggest that these are determined by the same type of unobserved heterogeneity, which we attribute to the same unobserved process of decision-making. We develop and estimate a theoretical model of risky choices and mental health, in which mental health disparity across groups is generated by different degrees of self-control problems. Our findings imply that mental health concerns cannot be used to justify restrictive abortion policies. Moreover, potential self-control problems should be targeted as early as possible to combat future mental health consequences.

In the context of nonlinear prices, the empirical evidence suggests that the consumers have cognitive biases represented in a limited understanding of nonlinear price structures, and they respond to some alternative perceptions of the marginal prices. In particular, consumers usually make choices based more on the average than the marginal prices, which can result in a suboptimal behavior. Taking the misspecification in the marginal price as exogenous, this document analyzes how is the optimal quadratic price scheme for a monopolist and the optimal quadratic price scheme that maximizes welfare when there is a continuum of representative consumers with an arbitrary perception of the marginal price. Under simple preferences and costs functional forms and very straightforward hypotheses, the results suggest that the bias in the marginal price doesn't affect the maximum welfare attainable with quadratic price schemes, and it has a negligible effect over the efficiency cost caused by the monopolist, so the misspecification in the marginal price is not relevant for welfare increasing policies. However, almost always the misspecification in the marginal price is beneficial for the monopolist. An interesting result is that under these functional forms, more misspecification in the marginal price is beneficial for both the consumers and the monopolist if the level of bias is low, so not always is socially optima to have educated consumers about the real marginal price. Finally, the document shows that the bias in the marginal price has a negative effect on reduction of aggregate consumption using two-tier increasing tariffs, which are commonly used for reduction of aggregate consumption.

We develop a quantitative framework for understanding the class of wicked problems that emerge at the intersections of natural, social, and technological complex systems. Wicked problems reflect our incomplete understanding of interdependent global systems and the hyper-risk they pose; such problems escape solutions because they are often ill-defined and thus mis-identified and under-appreciated by problem-solvers and the communities they constitute. Because cross-boundary problems can be dissected from various viewpoints, such diversity can nevertheless contribute confusion to the collective understanding of the problem. We illustrate this paradox by analyzing the development of both topical and scholarly communities within three wicked domains: deforestation, invasive species, and wildlife trade research. Informed by comprehensive bibliometric analysis of both topical and collaboration communities emerging within and around each domain, we identify symptomatic characteristics of wicked uncertainty based upon quantitative assessment of consolidation or diversification of knowledge trajectories representing each domain. We argue that such knowledge trajectories are indicative of the underlying uncertainties of each research domain, which tend to exacerbate the wickedness of the problem itself. Notably, our results indicate that wildlife trade may become a neglected wicked problem due to high uncertainty, research paucity, and delayed knowledge consolidation.

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.

We prove three theorems about the exact solutions of a generalized or interacting Black-Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number $A_N(T)$. The first theorem states that if $A_N(T) = 0$, then the solution at the maturity of the interacting equation is identical to the solution of the free Black-Scholes equation with the same initial interest rate $r$. The second theorem states that if $A_N(T) \ne 0$, the solution can be expressed in terms of all higher derivatives of solutions to the free Black-Scholes equation with the initial interest rate $r$. The third theorem states that whatever the arbitrage number is, the solution is a solution to the free Black-Scholes equation with a variable interest rate $r(\tau) = r + (1/\tau) A_N(\tau)$. Also, we show, by using the Feynman-Kac theorem, that for the special case of a Call contract, the exact solution for a Call with strike price $K$ is equivalent to the usual Call solution to the Black-Scholes equation with strike price $\tilde{K} = K e^{-A_N(T)}$.

An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family.