We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an exponential, giving rise to long memory effects. In comparison with other available methods present in the literature, our procedure does not rely on subjective evaluations and is computationally inexpensive. The underlying basic idea is to use a suitable factor model to analyse the residual memory after sequentially removing more and more components, and stopping the process when the maximum amount of memory has been accounted for by the retained components. We validate our methodology on both synthetic and real financial data, and find in all cases a clear and computationally superior answer entirely compatible with available heuristic criteria, such as cumulative variance and cross-validation.

We conduct a sequential social learning experiment where subjects guess a hidden state after observing 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. Later agents' accuracy gains from social learning are twice as large in the sparse treatment compared to the dense treatment. Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the result is difficult to reconcile with rational-learning models.

Conic martingales refer to Brownian martingales evolving between bounds. Among other potential applications, they have been suggested for the sake of modeling conditional survival probabilities under partial information, as usual in reduced-form models. Yet, conic martingale default models have a special feature; in contrast to the class of Cox models, they fail to satisfy the so-called \emph{immersion property}. Hence, it is not clear whether this setup is arbitrage-free or not. In this paper, we study the relevance of conic martingales-driven default models for practical applications in credit risk modeling. We first introduce an arbitrage-free conic martingale, namely the $\Phi$-martingale, by showing that it fits in the class of Dynamized Gaussian copula model of Cr\'epey et al., thereby providing an explicit construction scheme for the default time. In particular, the $\Phi$-martingale features interesting properties inherent on its construction easing the practical implementation. Eventually, we apply this model to CVA pricing under wrong-way risk and CDS options, and compare our results with the JCIR++ (a.k.a. SSRJD) and TC-JCIR recently introduced as an alternative.

In this paper, we extend the model of Gao and Su (2016) and consider an omnichannel strategy in which inventory can be replenished when a retailer sells only in physical stores. With "buy-online-and-pick-up-in-store" (BOPS) having been introduced, consumers can choose to buy directly online, buy from a retailer using BOPS, or go directly to a store to make purchases without using BOPS. The retailer is able to select the inventory level to maximize the probability of inventory availability at the store. Furthermore, the retailer can incur an additional cost to reduce the BOPS ordering lead time, which results in a lowered hassle cost for consumers who use BOPS. In conclusion, we found that there are two types of equilibrium: that in which all consumers go directly to the store without using BOPS and that in which all consumers use BOPS.

Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the least-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over GLM and GAM methods to MARS and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.

This paper employs machine learning algorithms to forecast German electricity spot market prices. The forecasts utilize in particular bid and ask order book data from the spot market but also fundamental market data like renewable infeed and expected demand. Appropriate feature extraction for the order book data is developed. Using cross-validation to optimise hyperparameters, neural networks and random forests are proposed and compared to statistical reference models. The machine learning models outperform traditional approaches.

We consider a stochastic game-theoretic model of an investment market in continuous time with short-lived assets and study strategies, called survival, which guarantee that the relative wealth of an investor who uses such a strategy remains bounded away from zero. The main results consist in obtaining a sufficient condition for a strategy to be survival and showing that all survival strategies are asymptotically close to each other. It is also proved that a survival strategy allows an investor to accumulate wealth in a certain sense faster than competitors.