We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem (infimum over market measures, supremum over the control) at each instance. Moreover, the underlying Bellman equations are intrinsically multi-dimensional. We propose a novel machine learning approach that solves for the local saddle-point at a chosen set of inputs and then uses a nonparametric (Gaussian process) regression to obtain a functional representation of the value function. Our algorithm resembles control randomization and regression Monte Carlo techniques but also brings multiple innovations, including adaptive experimental design, separate surrogates for optimal control and the local worst-case measure, and computational speed-ups for the sup-inf optimization. Thanks to the new scheme we are able to consider settings that have been previously computationally intractable and provide several new financial insights about learning and optimal trading under unknown market parameters. In particular, we demonstrate the financial advantages of adaptive robust framework compared to adaptive and static robust alternatives.

Insurance companies make extensive use of Monte Carlo simulations in their capital and solvency models. To overcome the computational problems associated with Monte Carlo simulations, most large life insurance companies use proxy models such as replicating portfolios.

In this paper, we present an example based on a variable annuity guarantee, showing the main challenges faced by practitioners in the construction of replicating portfolios: the feature engineering step and subsequent basis function selection problem.

We describe how neural networks can be used as a proxy model and how to apply risk-neutral pricing on a neural network to integrate such a model into a market risk framework. The proposed model naturally solves the feature engineering and feature selection problems of replicating portfolios.

We refine the analysis of hedging strategies for options under the SABR model carried out in [2]. In particular, we provide a theoretical justification of the empirical observation made in [2] that the modified delta ("Bartlett's delta") introduced there provides a more accurate and robust hedging strategy than the conventional SABR delta hedge.

To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that differs from the pre-committed and game-theoretic strategies. A comparison with the existing results on the continuous time mean-variance model shows that our method has several advantages. The explicit solutions of the dynamic optimal strategy and optimal wealth are given. When the dynamic optimal strategy is given at the initial time, we do not change it in the following investment time interval.

We introduce a non linear pricing model of individual stock returns that defines a stickiness parameter of the returns. The pricing model resembles the capital asset pricing model used in finance but has a non linear component inspired from models of earth quake tectonic plate movements. The link to tectonic plate movements happens, since price movements of a given stock index is seen adding stress to its components of individual stock returns, in order to follow the index. How closely individual stocks follow the indexs price movements, can then be used to define their stickiness

Differential machine learning (ML) extends supervised learning, with models trained on examples of not only inputs and labels, but also differentials of labels to inputs.

Differential ML is applicable in all situations where high quality first order derivatives wrt training inputs are available. In the context of financial Derivatives risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential ML, combined with AAD, provides extremely effective pricing and risk approximations. We can produce fast pricing analytics in models too complex for closed form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or capital regulations.

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, resulting in vastly improved performance, illustrated with a number of numerical examples, both idealized and real world. In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results.

This paper is meant to be read in conjunction with its companion GitHub repo https://github.com/differential-machine-learning, where we posted a TensorFlow implementation, tested on Google Colab, along with examples from the article and additional ones. We also posted appendices covering many practical implementation details not covered in the paper, mathematical proofs, application to ML models besides neural networks and extensions necessary for a reliable implementation in production.

We introduce a new methodology that enables detection of the onset of convergence towards Nash equilibria in simple repeated games with infinitely large strategy spaces, thereby revealing the heuristics used in decision-making. The method works by constraining on a special finite subset of strategies, called decoupled strategies. We show how the technique can be applied to understand price formation in financial market experiments by introducing a predictive measure {\Delta}D: the different between positive decoupled strategies (recommending to buy) and negative decoupled strategies (recommending to sell). Using {\Delta}D we illustrate how the method can predict (at certain special times) participants' actions with a high success rate in a series of experiments

The COVID-19 pandemic has completely disrupted the operation of our societies. Its elusive transmission process, characterized by an unusually long incubation period, as well as a high contagion capacity, has forced many countries to take quarantine and social isolation measures that conspire against the performance of national economies. This situation confronts decision makers in different countries with the alternative of reopening the economies, thus facing the unpredictable cost of a rebound of the infection. This work tries to offer an initial theoretical framework to handle this alternative.

We investigate structural change in the PR China during a period of particularly rapid growth 1998-2014. For this, we utilize sectoral data from the World Input-Output Database and firm-level data from the Chinese Industrial Enterprise Database. Starting with correlation laws known from the literature (Fabricant's laws), we investigate which empirical regularities hold at the sectoral level and show that many of these correlations cannot be recovered at the firm level. For a more detailed analysis, we propose a multi-level framework, which is validated with empirically. For this, we perform a robust regression, since various input variables at the firm-level as well as the residuals of exploratory OLS regressions are found to be heavy-tailed. We conclude that Fabricant's laws and other regularities are primarily characteristics of the sectoral level which rely on aspects like infrastructure, technology level, innovation capabilities, and the knowledge base of the relevant labor force. We illustrate our analysis by showing the development of some of the larger sectors in detail and offer some policy implications in the context of development economics, evolutionary economics, and industrial organization.

Modern decision-making in fixed income asset management benefits from intelligent systems, which involve the use of state-of-the-art machine learning models and appropriate methodologies. We conduct the first study of bond yield forecasting using long short-term memory (LSTM) networks, validating its potential and identifying its memory advantage. Specifically, we model the 10-year bond yield using univariate LSTMs with three input sequences and five forecasting horizons. We compare those with multilayer perceptrons (MLP), univariate and with the most relevant features. To demystify the notion of black box associated with LSTMs, we conduct the first internal study of the model. To this end, we calculate the LSTM signals through time, at selected locations in the memory cell, using sequence-to-sequence architectures, uni and multivariate. We then proceed to explain the states' signals using exogenous information, for what we develop the LSTM-LagLasso methodology. The results show that the univariate LSTM model with additional memory is capable of achieving similar results as the multivariate MLP using macroeconomic and market information. Furthermore, shorter forecasting horizons require smaller input sequences and vice-versa. The most remarkable property found consistently in the LSTM signals, is the activation/deactivation of units through time, and the specialisation of units by yield range or feature. Those signals are complex but can be explained by exogenous variables. Additionally, some of the relevant features identified via LSTM-LagLasso are not commonly used in forecasting models. In conclusion, our work validates the potential of LSTMs and methodologies for bonds, providing additional tools for financial practitioners.

This study examines whether the efficiency of cryptocurrency markets (Bitcoin and Ethereum) evolve over time based on Lo's (2004) adaptive market hypothesis (AMH). In particular, we measure the degree of market efficiency using a generalized least squares-based time-varying model that does not depend on sample size, unlike previous studies that used conventional methods. The empirical results show that (1) the degree of market efficiency varies with time in the markets, (2) Bitcoin's market efficiency level is higher than that of Ethereum over most periods, and (3) a market with high market liquidity has been evolving. We conclude that the results support the AMH for the most established cryptocurrency market.