We propose a mean field game model to study the question of how centralization of reward and computational power occur in the Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, or a "rich get richer" effect. This concentration phenomenon is aggravated by a higher bitcoin price, and reduced by competition. Additionally, an advanced miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies.

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard "flat-view" multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduce a tensor-valued approach to model the global risks shared by multiple interest rate curves. In this way, the estimated risk factors can be analytically decomposed into maturity-domain and country-domain constituents, which allows the investor to devise rigorous and tractable global portfolio management and hedging strategies tailored to each risk domain. An empirical analysis confirms the existence of global risk factors shared by eight developed economies, and demonstrates their ability to compactly describe the global macroeconomic environment.

We propose a mathematical model of momentum risk-taking, which is essentially real-time risk management, and discuss its implementation: an automated momentum equity trading system. Risk-taking is one of the key components of general decision-making, a challenge for artificial intelligence and machine learning; stock markets are quite a test for any risk-management theories. We begin with a relatively simple continuous model of news impact on share-prices. In spite of its simplicity, it describes well the power growth of share-prices, periodicity, logarithmic periodicity, and the market phenomena like using price targets and profit-taking; Bessel and hypergeometric functions are used. Its discretization is performed, adjusted to discontinuous functions and aimed at stock charts, the main examples for us. An automated trading system based on our approach proved to be successful in extensive historical and real-time experiments. Its preimage is a new contract card game presented at the end, a combination of bridge and poker.

As the decade turns, we reflect on nearly thirty years of successful manipulation of the world's public equity markets. This reflection highlights a few of the key enabling ingredients and lessons learned along the way. A quantitative understanding of market impact and its decay, which we cover briefly, lets you move long-term market prices to your advantage at acceptable cost. Hiding your footprints turns out to be less important than moving prices in the direction most people want them to move. Widespread (if misplaced) trust of market prices -- buttressed by overestimates of the cost of manipulation and underestimates of the benefits to certain market participants -- makes price manipulation a particularly valuable and profitable tool. Of the many recent stories heralding the dawn of the present golden age of misinformation, the manipulation leading to the remarkable increase in the market capitalization of the world's publicly traded companies over the past three decades is among the best.

We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled decision problems (one for each player) and solve them iteratively. The individual decision problem is characterized by a semilinear Hamilton-Jacobi-Bellman equation, to solve which we employ the recently developed deep BSDE method. The resulted algorithm can solve large $N$-player games for which conventional numerical methods would suffer from the curse of dimensionality. Multiple numerical examples involving identical or heterogeneous agents, with risk-neutral or risk-sensitive objectives, are tested to validate the accuracy of the proposed algorithm in large group games. Even for a fifty-player game with the presence of common noise, the proposed algorithm still finds the approximate Nash equilibrium accurately, which, to our best knowledge, is difficult to achieve by other numerical algorithms.

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Le\~ao, Ohashi and Russo and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed.

In recent years, it has been debated whether a reduction in working hours would be a viable solution to tackle the unemployment caused by technological change. The improvement of existing production technology is gradually being seen to reduce labor demand. Although this debate has been at the forefront for many decades, the high and persistent unemployment encountered in the European Union has renewed interest in implementing this policy in order to increase employment. According to advocates of reducing working hours, this policy will increase the number of workers needed during the production process, increasing employment. However, the contradiction expressed by advocates of working time reduction is that the increase in labor costs will lead to a reduction in business activity and ultimately to a reduction in demand for human resources. In this article, we will attempt to answer the question of whether reducing working hours is a way of countering the potential decline in employment due to technological change. In order to answer this question, the aforementioned conflicting views will be examined. As we will see during our statistical examination of the existing empirical studies, the reduction of working time does not lead to increased employment and cannot be seen as a solution to the long-lasting unemployment.

Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of \emph{insider information}. We assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy. In particular, we show that the value of the insider information may be bounded while the arbitrage condition holds and we prove that the insider information does not always imply arbitrage for the insider by providing an explicit example.

In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this kind of problem, we consider to minimize the variances of the investment portfolio at multi-time state. The advantage of this multi-time state mean-variance model is that we can minimize the risk of the investment portfolio along the investment period. To obtain the optimal strategy of the multi-time state mean-variance model, we introduce a sequence of Riccati equations which are connected by a jump boundary condition. Based on this sequence Riccati equations, we establish the relationship between the means and variances of this multi-time state mean-variance model. Furthermore, we use an example to verify that minimizing the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler-Maruyama type scheme. We show that our methods allow to obtain efficient and accurate European and American option prices. Numerical experiments are provided, and show the reliability and the efficiency of the algorithms.

Since the introduction of risk-based solvency regulation, pro-cyclicality has been a subject of concerns from all market participants. Here, we lay down a methodology to evaluate the amount of pro-cyclicality in the way finnancial institutions measure risk, and identify factors explaining this pro-cyclical behavior. We introduce a new indicator based on the Sample Quantile Process (SQP, a dynamic generalization of Value-at-Risk), conditioned on realized volatility to quantify the pro-cyclicality, and evaluate its amount in the markets, considering 11 stock indices as realizations of the SQP. Then we determine two main factors explaining the pro-cyclicality: the clustering and return-to-the-mean of volatility, as it could have been anticipated but not quantified before, and, more surprisingly, the very way risk is measured, independently of this return-to-the-mean effect.