In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks. As some additional applications, we consider anomaly detection and automatic generation of financial data.

Mid-price movement prediction based on limit order book (LOB) data is a challenging task due to the complexity and dynamics of the LOB. So far, there have been very limited attempts for extracting relevant features based on LOB data. In this paper, we address this problem by designing a new set of handcrafted features and performing an extensive experimental evaluation on both liquid and illiquid stocks. More specifically, we implement a new set of econometrical features that capture statistical properties of the underlying securities for the task of mid-price prediction. Moreover, we develop a new experimental protocol for online learning that treats the task as a multi-objective optimization problem and predicts i) the direction of the next price movement and ii) the number of order book events that occur until the change takes place. In order to predict the mid-price movement, the features are fed into nine different deep learning models based on multi-layer perceptrons (MLP), convolutional neural networks (CNN) and long short-term memory (LSTM) neural networks. The performance of the proposed method is then evaluated on liquid and illiquid stocks, which are based on TotalView-ITCH US and Nordic stocks, respectively. For some stocks, results suggest that the correct choice of a feature set and a model can lead to the successful prediction of how long it takes to have a stock price movement.

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate $r$. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.

This paper proposes a theory of pricing consistent with two well-documented patterns: customers care about fairness, and firms take these concerns into account when they set prices. The theory assumes that customers find a price unfair when it carries a high markup over cost, and that customers dislike unfair prices. Since markups are not observable, customers must extract them from prices. The theory assumes that customers infer less than rationally: when a price rises after an increase in marginal cost, customers partially misattribute the higher price to a higher markup---which they find unfair. Firms anticipate this response and trim their price increases, which reduces the passthrough of marginal costs into prices below one: prices are somewhat rigid. Embedded in a New Keynesian model---as a replacement of Calvo pricing---our theory produces monetary nonneutrality. When monetary policy loosens and inflation rises, customers misperceive markups as higher and feel unfairly treated; firms mitigate the perceived unfairness of prices by reducing their markups, which in general equilibrium leads to higher output.

In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes as a function of the dynamic optimization parameters in the context of Markov decision processes. We call this analysis stochastic comparative statics. We derive both comparative statics results and stochastic comparative statics results showing how the current and future optimal decisions change in response to changes in the single-period payoff function, the discount factor, the initial state of the system, and the transition probability function. We apply our results to various models from the economics and operations research literature, including investment theory, dynamic pricing models, controlled random walks, and comparisons of stationary distributions.

A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can be calibrated to the initial yield curve and other market data. Our analysis suggests that strict local martingales can be used for modelling the pricing kernels associated with virtual currencies based on distributed ledger technologies.

The transport sector is witnessing unprecedented levels of disruption. Privately owned cars that operate on internal combustion engines have been the dominant modes of passenger transport for much of the last century. However, recent advances in transport technologies and services, such as the development of autonomous vehicles, the emergence of shared mobility services, and the commercialization of alternative fuel vehicle technologies, promise to revolutionise how humans travel. The implications are profound: some have predicted the end of private car dependent Western societies, others have portended greater suburbanization than has ever been observed before. If transport systems are to fulfil current and future needs of different subpopulations, and satisfy short and long-term societal objectives, it is imperative that we comprehend the many factors that shape individual behaviour. This chapter introduces the technologies and services most likely to disrupt prevailing practices in the transport sector. We review past studies that have examined current and future demand for these new technologies and services, and their likely short and long-term impacts on extant mobility patterns. We conclude with a summary of what these new technologies and services might mean for the future of mobility.