An artificial general intelligence (AGI) might have an instrumental drive to modify its utility function to improve its ability to cooperate, bargain, promise, threaten, and resist and engage in blackmail. Such an AGI would necessarily have a utility function that was at least partially observable and that was influenced by how other agents chose to interact with it. This instrumental drive would conflict with the orthogonality thesis since the modifications would be influenced by the AGI's intelligence. AGIs in highly competitive environments might converge to having nearly the same utility function, one optimized to favorably influencing other agents through game theory.

The cryptocurrency market is amongst the fastest-growing of all the financial markets in the world. Unlike traditional markets, such as equities, foreign exchange and commodities, cryptocurrency market is considered to have larger volatility and illiquidity. This paper is inspired by the recent success of using deep learning for stock market prediction. In this work, we analyze and present the characteristics of the cryptocurrency market in a high-frequency setting. In particular, we applied a deep learning approach to predict the direction of the mid-price changes on the upcoming tick. We monitored live tick-level data from $8$ cryptocurrency pairs and applied both statistical and machine learning techniques to provide a live prediction. We reveal that promising results are possible for cryptocurrencies, and in particular, we achieve a consistent $78\%$ accuracy on the prediction of the mid-price movement on live exchange rate of Bitcoins vs US dollars.

Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show that, in most cases, adding further constraints gives rise to bounds that are considerably tighter and discuss the maximizing/minimizing copulas achieving such bounds. Our approach follows the literature on constrained optimal transport and, in particular, builds on a recent paper by Eckstein and Kupper (2019, Appl. Math. Optim.).

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and sell prices that hold in total analogy to the properties of the scalar indifference prices for complete preferences. We show how the (weak and strong) set-valued certainty equivalent as well as the indifference price bounds can be computed or approximated by solving convex vector optimization problems. Numerical examples and their economic interpretations are given for the univariate as well as for the multivariate case.

The importance of supply chain management in analyzing and later catalyzing economic expectations while simultaneously prioritizing cleaner production aspects is a vital component of modern finance. Such predictions, though, are often known to be less than accurate due to the ubiquitous uncertainty plaguing most business decisions. Starting from a multi-dimensional cost function defining the sustainability of the supply chain (SC) kernel, this article outlines a 4-component SC module - environmental, demand, economic, and social uncertainties - each ranked according to its individual weight. Our mathematical model then assesses the viability of a sustainable business by first ranking the potentially stochastic variables in order of their subjective importance, and then optimizing the cost kernel, defined from a utility function. The model will then identify conditions (as equations) validating the sustainability of a business venture. The ranking is initially obtained from an Analytical Hierarchical Process; the resultant weighted cost function is then optimized to analyze the impact of market uncertainty based on our supply chain model. Model predictions are then ratified against SME data to emphasize the importance of cleaner production in business strategies.

We investigate the possibility of completing financial markets in a model with no exogenous probability measure and market imperfections. A necessary and sufficient condition is obtained for such extension to be possible.

We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional convergence to a continuous space - discrete time model. Then, we show a thermodynamic limit of the empirical distribution to the solution of a kinetic equation of Boltzmann type. We solve this equation and we show that the solutions coincide with the appropriate limits of the invariant measure for the Markov chain. In this way we complete Boltzmann's program of deriving kinetic equations from random dynamics for this simple model. Three families of invariant measures for the mean field limit are discovered and we show that only two of those families can be obtained as limits of the discrete system and the third is extraneous. Finally, we cast our results in the framework of integer partitions and strengthen some results already available in the literature.

Financial time-series analysis and forecasting have been extensively studied over the past decades, yet still remain as a very challenging research topic. Since financial market is inherently noisy and stochastic, a majority of financial time-series of interests are non-stationary, and often obtained from different modalities. This property presents great challenges and can significantly affect the performance of the subsequent analysis/forecasting steps. Recently, the Temporal Attention augmented Bilinear Layer (TABL) has shown great performances in tackling financial forecasting problems. In this paper, by taking into account the nature of bilinear projections in TABL networks, we propose Bilinear Normalization (BiN), a simple, yet efficient normalization layer to be incorporated into TABL networks to tackle potential problems posed by non-stationarity and multimodalities in the input series. Our experiments using a large scale Limit Order Book (LOB) consisting of more than 4 millions order events show that BiN-TABL outperforms TABL networks using other state-of-the-arts normalization schemes by a large margin.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

We develop a dynamic decomposition of the empirical Beveridge curve, i.e., the level of vacancies conditional on unemployment. Using a standard model, we show that three factors can shift the Beveridge curve: reduced-form matching efficiency, changes in the job separation rate, and out-of-steady-state dynamics. We find that the shift in the Beveridge curve during and after the Great Recession was due to all three factors, and each factor taken separately had a large effect. Comparing the pre-2010 period to the post-2010 period, a fall in matching efficiency and out-of-steady-state dynamics both pushed the curve upward, while the changes in the separation rate pushed the curve downward. The net effect was the observed upward shift in vacancies given unemployment. In previous recessions changes in matching efficiency were relatively unimportant, while dynamics and the separation rate had more impact. Thus, the unusual feature of the Great Recession was the deterioration in matching efficiency, while separations and dynamics have played significant, partially offsetting roles in most downturns. The importance of these latter two margins contrasts with much of the literature, which abstracts from one or both of them. We show that these factors affect the slope of the empirical Beveridge curve, an important quantity in recent welfare analyses estimating the natural rate of unemployment.

In this paper we study a continuous time equilibrium model of limit order book (LOB) in which the liquidity dynamics follows a non-local, reflected mean-field stochastic differential equation (SDE) with evolving intensity. Generalizing the basic idea of Ma et al. (2015), we argue that the frontier of the LOB (e.g., the best asking price) is the value function of a mean-field stochastic control problem, as the limiting version of a Bertrand-type competition among the liquidity providers. With a detailed analysis on the $N$-seller static Bertrand game, we formulate a continuous time limiting mean-field control problem of the representative seller. We then validate the dynamic programming principle (DPP), and show that the value function is a viscosity solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We argue that the value function can be used to obtain the equilibrium density function of the LOB, following the idea of Ma et al. (2015).

We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics.

A risk-averse agent hedges her exposure to a non-tradable risk factor $U$ using a correlated traded asset $S$ and accounts for the impact of her trades on both factors. The effect of the agent's trades on $U$ is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in $U$. When the exposure to the non-tradable risk factor $\psi(U_T)$ is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when $\psi(U_T)$ is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.

In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are studied. Numerical results are provided to validate the theoretical work.

We find economically and statistically significant gains from using machine learning to dynamically allocate between the market index and the risk-free asset. We model the market price of risk to determine the optimal weights in the portfolio: reward-risk market timing. This involves forecasting the direction of next month's excess return, which gives the reward, and constructing a dynamic volatility estimator that is optimized with a machine learning model, which gives the risk. Reward-risk timing with machine learning provides substantial improvements in investor utility, alphas, Sharpe ratios, and maximum drawdowns, after accounting for transaction costs, leverage constraints, and on a new out-of-sample test set. This paper provides a unifying framework for machine learning applied to both return- and volatility-timing.

In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We use the expected number of jump misclassifications as the objective function to optimally select the threshold parameter of the jump detection scheme. We prove that the objective function is quasi-convex and obtain a new second-order infill approximation of the optimal threshold in closed form. The approximate optimal threshold depends not only on the spot volatility, but also the jump intensity and the value of the jump density at the origin. Estimation methods for these quantities are then developed, where the spot volatility is estimated by a kernel estimator with thresholding and the value of the jump density at the origin is estimated by a density kernel estimator applied to those increments deemed to contain jumps by the chosen thresholding criterion. Due to the interdependency between the model parameters and the approximate optimal estimators built to estimate them, a type of iterative fixed-point algorithm is developed to implement them. Simulation studies for a prototypical stochastic volatility model show that it is not only feasible to implement the higher-order local optimal threshold scheme but also that this is superior to those based only on the first order approximation and/or on average values of the parameters over the estimation time period.

We propose a simple model where the innovation rate of a technological domain depends on the innovation rate of the technological domains it relies on. Using data on US patents from 1836 to 2017, we make out-of-sample predictions and find that the predictability of innovation rates can be boosted substantially when network effects are taken into account. In the case where a technology$'$s neighborhood future innovation rates are known, the average predictability gain is 28$\%$ compared to simpler time series model which do not incorporate network effects. Even when nothing is known about the future, we find positive average predictability gains of 20$\%$. The results have important policy implications, suggesting that the effective support of a given technology must take into account the technological ecosystem surrounding the targeted technology.

We introduce a new deep learning architecture for predicting price movements from limit order books. This architecture uses a causal convolutional network for feature extraction in combination with masked self-attention to update features based on relevant contextual information. This architecture is shown to significantly outperform existing architectures such as those using convolutional networks (CNN) and Long-Short Term Memory (LSTM) establishing a new state-of-the-art benchmark for the FI-2010 dataset.