Presidential debates are thought to provide an important public good by revealing information on candidates to voters. However, this may not always be the case. We consider an endogenous model of presidential debates in which an incumbent and a contender (who is privately informed about her own quality) publicly announce whether they are willing to participate in a public debate, after taking into account that a voter's choice of candidate depends on her beliefs regarding the candidates' qualities and on the state of nature. Surprisingly, it is found that in equilibrium a debate occurs or does not occur independently of the contender's quality or the sequence of the candidates' announcements to participate and therefore the announcements are uninformative.

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.

Empirical investor networks (EIN) proposed by \cite{Ozsoylev-Walden-Yavuz-Bildik-2014-RFS} are assumed to capture the information spreading path among investors. Here, we perform a comparative analysis between the EIN and the cellphone communication networks (CN) to test whether EIN is an information exchanging network from the perspective of the layer structures of ego networks. We employ two clustering algorithms ($k$-means algorithm and $H/T$ break algorithm) to detect the layer structures for each node in both networks. We find that the nodes in both networks can be clustered into two groups, one that has a layer structure similar to the theoretical Dunbar Circle corresponding to that the alters in ego networks exhibit a four-layer hierarchical structure with the cumulative number of 5, 15, 50 and 150 from the inner layer to the outer layer, and the other one having an additional inner layer with about 2 alters compared with the Dunbar Circle. We also find that the scale ratios, which are estimated based on the unique parameters in the theoretical model of layer structures \citep{Tamarit-Cuesta-Dunbar-Sanchez-2018-PNAS}, conform to a log-normal distribution for both networks. Our results not only deepen our understanding on the topological structures of EIN, but also provide empirical evidence of the channels of information diffusion among investors.

We consider the estimation of binary election outcomes as martingales and propose an arbitrage pricing when one continuously updates estimates. We argue that the estimator needs to be priced as a binary option as the arbitrage valuation minimizes the conventionally used Brier score for tracking the accuracy of probability assessors.

We create a dual martingale process $Y$, in $[L,H]$ from the standard arithmetic Brownian motion, $X$ in $(-\infty, \infty)$ and price elections accordingly. The dual process $Y$ can represent the numerical votes needed for success.

We show the relationship between the volatility of the estimator in relation to that of the underlying variable. When there is a high uncertainty about the final outcome, 1) the arbitrage value of the binary gets closer to 50\%, 2) the estimate should not undergo large changes even if polls or other bases show significant variations.

There are arbitrage relationships between 1) the binary value, 2) the estimation of $Y$, 3) the volatility of the estimation of $Y$ over the remaining time to expiration. We note that these arbitrage relationships were often violated by the various forecasting groups in the U.S. presidential elections of 2016, as well as the notion that all intermediate assessments of the success of a candidate need to be considered, not just the final one.

This paper is concerned with a two-fold objective. Firstly, we establish elicitability and identifiability results for systemic risk measures introduced in Feinstein, Rudloff and Weber (2017). Specifying the entire set of capital allocations adequate to render a financial system acceptable, these systemic risk measures are examples of set-valued functionals. A functional is elicitable (identifiable) if it is the unique minimiser (zero) of an expected scoring function (identification function). Elicitability and identifiability are essential for forecast ranking and validation, $M$- and $Z$-estimation, both possibly in a regression framework. To account for the set-valued nature of the systemic risk measures mentioned above, we secondly introduce a theoretical framework of elicitability and identifiability of set-valued functionals. It distinguishes between exhaustive forecasts, being set-valued and aiming at correctly specifying the entire functional, and selective forecasts, content with solely specifying a single point in the correct functional. Uncovering the structural relation between the two corresponding notions of elicitability and identifiability, we establish that a set-valued functional can be either selectively elicitable or exhaustively elicitable. Notably, selections of quantiles such as the lower quantile turn out not to be elicitable in general. Applying these structural results to systemic risk measures, we construct oriented selective identification functions, which induce a family of strictly consistent exhaustive elementary scoring functions. We discuss equivariance properties of these scores. We demonstrate their applicability in a simulation study considering comparative backtests of Diebold-Mariano type with a pointwise traffic-light illustration of Murphy diagrams.

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks a price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or characterizations to the bookmaker's optimal bookmaking problem in various interesting models.

Portfolio allocation is crucial for investment companies. However, getting the best strategy in a complex and dynamic stock market is challenging. In this paper, we propose a novel Adaptive Deep Deterministic Reinforcement Learning scheme (Adaptive DDPG) for the portfolio allocation task, which incorporates optimistic or pessimistic deep reinforcement learning that is reflected in the influence from prediction errors. Dow Jones 30 component stocks are selected as our trading stocks and their daily prices are used as the training and testing data. We train the Adaptive DDPG agent and obtain a trading strategy. The Adaptive DDPG's performance is compared with the vanilla DDPG, Dow Jones Industrial Average index and the traditional min-variance and mean-variance portfolio allocation strategies. Adaptive DDPG outperforms the baselines in terms of the investment return and the Sharpe ratio.

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty bond, but is confident that it lies within a uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super-replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

In most OTC markets, a small number of market makers provide liquidity to clients from the buy side. More precisely, they set prices at which they agree to buy and sell the assets they cover. Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money out of their bid-ask spread while mitigating the risk associated with holding inventory in a volatile market. Many market making models have been proposed in the academic literature, most of them dealing with single-asset market making whereas market makers are usually in charge of a long list of assets. The rare models tackling multi-asset market making suffer however from the curse of dimensionality when it comes to the numerical approximation of the optimal quotes. The goal of this paper is to propose a dimensionality reduction technique to address multi-asset market making with grid methods. Moreover, we generalize existing market making models by the addition of an important feature for OTC markets: the variability of transaction sizes and the possibility for the market maker to answer different prices to requests with different sizes.

In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We use the dependence structure of the correlations network in constructing some well-known risk-based models in which the estimation of correlation matrix is a building block in the portfolio optimization. We formulate and solve all these portfolio allocation problems using both the standard approach and the network-based approach. Moreover, in constructing the network-based portfolios we propose the use of two different estimators for the covariance matrix: the sample estimator and the shrinkage toward constant correlation one. All the strategies under analysis are implemented on two high-dimensional portfolios having different characteristics, covering the period from January $2001$ to December $2017$. We find that the network-based portfolio consistently better performs and has lower risk compared to the corresponding standard portfolio in an out-of-sample perspective.

The possibility of re-switching of techniques in Piero Sraffa's intersectoral model, namely the returning capital-intensive techniques with monotonic changes in the profit rate, is traditionally considered as a paradox putting at stake the viability of the neoclassical theory of production. It is argued here that this phenomenon can be rationalized within the neoclassical paradigm. Sectoral interdependencies can give rise to non-monotonic effects of progressive variations in income distribution on relative prices. The re-switching of techniques is, therefore, the result of cost-minimizing technical choices facing returning ranks of relative input prices in full consistency with the neoclassical perspective.