We propose a novel approach to sentiment data filtering for a portfolio of assets. In our framework, a dynamic factor model drives the evolution of the observed sentiment and allows to identify two distinct components: a long-term component, modeled as a random walk, and a short-term component driven by a stationary VAR(1) process. Our model encompasses alternative approaches available in literature and can be readily estimated by means of Kalman filtering and expectation maximization. This feature makes it convenient when the cross-sectional dimension of the sentiment increases. By applying the model to a portfolio of Dow Jones stocks, we find that the long term component co-integrates with the market principal factor, while the short term one captures transient swings of the market associated with the idiosyncratic components and captures the correlation structure of returns. Finally, using quantile regressions, we assess the significance of the contemporaneous and lagged explanatory power of sentiment on returns finding strong statistical evidence when extreme returns, especially negative ones, are considered.

We introduce a concept of $autoregressive$ (AR)state-space realization that could be applied to all transfer functions $\boldsymbol{T}(L)$ with $\boldsymbol{T}(0)$ invertible. We show that a theorem of Kalman implies each Vector Autoregressive model (with exogenous variables) has a minimal $AR$-state-space realization of form $\boldsymbol{y}_t = \sum_{i=1}^p\boldsymbol{H}\boldsymbol{F}^{i-1}\boldsymbol{G}\boldsymbol{x}_{t-i}+\boldsymbol{\epsilon}_t$ where $\boldsymbol{F}$ is a nilpotent Jordan matrix and $\boldsymbol{H}, \boldsymbol{G}$ satisfy certain rank conditions. The case $VARX(1)$ corresponds to reduced-rank regression. Similar to that case, for a fixed Jordan form $\boldsymbol{F}$, $\boldsymbol{H}$ could be estimated by least square as a function of $\boldsymbol{G}$. The likelihood function is a determinant ratio generalizing the Rayleigh quotient. It is unchanged if $\boldsymbol{G}$ is replaced by $\boldsymbol{S}\boldsymbol{G}$ for an invertible matrix $\boldsymbol{S}$ commuting with $\boldsymbol{F}$. Using this invariant property, the search space for maximum likelihood estimate could be constrained to equivalent classes of matrices satisfying a number of orthogonal relations, extending the results in reduced-rank analysis. Our results could be considered a multi-lag canonical-correlation-analysis. The method considered here provides a solution in the general case to the polynomial product regression model of Velu et. al. We provide estimation examples. We also explore how the estimates vary with different Jordan matrix configurations and discuss methods to select a configuration. Our approach could provide an important dimensional reduction technique with potential applications in time series analysis and linear system identification. In the appendix, we link the reduced configuration space of $\boldsymbol{G}$ with a geometric object called a vector bundle.

We conduct a sequential social-learning experiment where subjects take turns guessing a hidden state based on private signals and the guesses of a subset of their predecessors. A network determines the observable predecessors, and we compare subjects' accuracy on sparse and dense networks. Accuracy gains from social learning are twice as large on sparse networks compared to dense networks. Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the finding is difficult to reconcile with rational-learning models.

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of 5 or 10. To illustrate the relevance of our results, we revisit the size and momentum anomalies.

The Credit Network is a model for transactions across a network of agents based on bilateral trust between agents. Credit Networks capture many aspects of traditional currencies as well as new virtual currencies and payment mechanisms. In a credit network, if an agent defaults, every other node that trusted it is vulnerable to loss. Alternatively, in a cryptocurrency context, securing a payment channel requires putting capital into escrow to guarantee against default. In this paper, we introduce constraints that bound the total amount of loss that the rest of the network can suffer if an agent (or a set of agents) were to default. We show that these constraints preserve two important aspects of credit networks. The first is route independence: if there are multiple trust-paths over which a transaction can clear, then it does not matter which one is used. The second pertains to liquidity (i.e. the fraction of transactions that succeed): given a symmetric transaction matrix, any achievable vector of net "credit balances" of the agents is equally likely. This technical property allows us to extend the original analysis of liquidity in credit networks to the constrained case. Surprisingly, aggregate borrowing constraints greatly simplify the analysis and achieve the optimal tradeoff between liquidity and the number of trust-edges.

In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distributions in the return series of Bitcoin. Comparative to the two distributions, the normal inverse Gaussian distribution captured adequately the fat tails and skewness in all the GARCH type models. The tGARCH model was the best model as it described the asymmetric occurrence of shocks in the Bitcoin market. That is, the response of investors to the same amount of good and bad news are distinct. From the empirical results, it can be concluded that tGARCH-NIG was the best model to estimate the volatility in the return series of Bitcoin. Generally, it would be optimal to use the NIG distribution in GARCH type models since time series of most cryptocurrency are leptokurtic.

Functions or 'functionings' enable to give a structure to any economic activity whether they are used to describe a good or a service that is exchanged on a market or they constitute the capability of an agent to provide the labor market with specific work and skills. That structure encompasses the basic law of supply and demand and the conditions of growth within a transaction and of the inflation control. Functional requirements can be followed from the design of a product to the delivery of a solution to a customer needs with different levels of externalities while value is created integrating organizational and technical constraints whereas a budget is allocated to the various entities of the firm involved in the production. Entering the market through that structure leads to designing basic equations of its dynamics and to finding canonical solutions out of particular equilibria. This approach enables to tackle behavioral foundations of Prospect Theory within a generalization of its probability weighting function turned into an operator which applies to Western, Educated, Industrialized, Rich, and Democratic societies as well as to the poorest ones. The nature of reality and well-being appears then as closely related to the relative satisfaction reached on the market, as it can be conceived by an agent, according to business cycles. This reality being the result of the complementary systems that govern human mind as structured by rational psychologists.

It is widely known that the common risk-factors derived from PCA beyond the first eigenportfolio are generally difficult to interpret and thus to use in practical portfolio management. We explore a alternative approach (HPCA) which makes strong use of the partition of the market into sectors. We show that this approach leads to no loss of information with respect to PCA in the case of equities (constituents of the S&P 500) and also that the associated common factors admit simple interpretations. The model can also be used in markets in which the sectors have asynchronous price information, such as single-name credit default swaps, generalizing the works of Cont and Kan (2011) and Ivanov (2016).

An important question in economics is how people choose between different payments in the future. The classical normative model predicts that a decision maker discounts a later payment relative to an earlier one by an exponential function of the time between them. Descriptive models use non-exponential functions to fit observed behavioral phenomena, such as preference reversal. Here we propose a model of discounting, consistent with standard axioms of choice, in which decision makers maximize the growth rate of their wealth. Four specifications of the model produce four forms of discounting -- no discounting, exponential, hyperbolic, and a hybrid of exponential and hyperbolic -- two of which predict preference reversal. Our model requires no assumption of behavioral bias or payment risk.

In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the so-called geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.

We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings both under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation that is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain.

This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit default risk. The external default contagion is considered in the sense that one default event can affect the default probabilities of all surviving subsidiaries. The total dividend problem is formulated for the insurance group and we reveal for the first time that the optimal singular dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier for each subsidiary is modulated by the current default state, namely how many and which subsidiaries have defaulted will determine the dividend threshold for each surviving subsidiary. These interesting conclusions are based on our analysis of the associated recursive system of Hamilton-Jacobi-Bellman variational inequalities (HJBVIs), which is new to the literature. The existence of the classical solution is established and the rigorous proof of the verification theorem is provided. For the case of two subsidiaries, the value function and optimal barriers for each subsidiary are explicitly constructed. Some numerical examples are also presented to illustrate the economic insights.

In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set $\Xi\subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in $\Xi$. For any Borel measurable claim $\xi$ which is bounded from below, the superhedging price coincides with the supremum over all pricing functionals $\mathbb{E}_{\mathbb{Q}}[\xi]$ with respect to martingale measures $\mathbb{Q}$ concentrated on the prediction set $\Xi$. This allows to include beliefs in future paths of the price process expressed by the set $\Xi$, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup.

A distinct set of disadvantages experienced by black Americans increases their likelihood of experiencing negative financial shocks, decreases their ability to mitigate the impact of such shocks, and ultimately results in debt collection cases being far more common in black neighborhoods than in non-black neighborhoods. In this paper, we create a novel dataset that links debt collection court cases with information from credit reports to document the disparity in debt collection judgments across black and non-black neighborhoods and to explore potential mechanisms that could be driving this judgment gap. We find that majority black neighborhoods experience approximately 40% more judgments than non-black neighborhoods, even after controlling for differences in median incomes, median credit scores, and default rates. The racial disparity in judgments cannot be explained by differences in debt characteristics across black and non-black neighborhoods, nor can it be explained by differences in attorney representation, the share of contested judgments, or differences in neighborhood lending institutions.

We solve in closed-form a Nash equilibrium model in which a finite number of exponential investors trade continuously with price-impact over a finite time horizon. By comparing our continuous-time Nash equilibrium model to the otherwise identical competitive Radner equilibrium model, we show that our Nash equilibrium model with price-impact can simultaneously help resolve the interest rate puzzle, the equity premium puzzle, and the stock volatility puzzle.

This paper acts as a collection of various trading strategies and useful pieces of market information that might help to implement such strategies. This list is meant to be comprehensive (though by no means exhaustive) and hence we only provide pointers and give further sources to explore each strategy further. To set the stage for this exploration, we consider the factors that determine good and bad trades, the notions of market efficiency, the real prospect amidst the seemingly high expectations of homogeneous expectations from human beings and the catch-22 connotations that arise while comprehending the true meaning of rational investing. We can broadly classify trading ideas and client market color material into Delta-One and Derivative strategies since this acts as a natural categorization that depends on the expertise of the various trading desks that will implement these strategies. For each strategy, we will have a core idea and we will present different flavors of this central theme to demonstrate that we can easily cater to the varying risk appetites, regional preferences, asset management styles, investment philosophies, liability constraints, investment horizons, notional trading size, trading frequency and other preferences of different market participants.

As an illustrative example, we consider in detail an investment strategy, titled "The Bounce Basket", designed for someone to express a bullish view on the market by allowing them to take long positions on securities that would benefit the most from a rally in the markets. The central idea of this theme is to identity securities from a regional perspective that are heavily shorted and yet are fundamentally sound with at least a minimum buy rating from a consensus of stock analysts covering the securities.