We consider continuous-time Mean-variance (MV) portfolio optimization problem in the Reinforcement Learning (RL) setting. The problem falls into the entropy-regularized relaxed stochastic control framework recently introduced in Wang et al. (2019). We derive the feedback exploration policy as the Gaussian distribution, with time-decaying variance. Close connections between the entropy-regularized MV and the classical MV are also discussed, including the solvability equivalence and the convergence as exploration decays. Finally, we prove a policy improvement theorem (PIT) for the continuous-time MV problem under both entropy regularization and control relaxation. The PIT leads to an implementable RL algorithm for the continuous-time MV problem. Our algorithm outperforms an adaptive control based method that estimates the underlying parameters in real-time and a state-of-the-art RL method that uses deep neural networks for continuous control problems by a large margin in nearly all simulations.

Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this research, we use deep generative models to develop two new semi-supervised Bayesian models for reject inference in credit scoring, in which we model the data generating process to be dependent on a Gaussian mixture. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. Our proposed models infer the unknown creditworthiness of the rejected applications by exact enumeration of the two possible outcomes of the loan (default or non-default). The efficient stochastic gradient optimization technique used in deep generative models makes our models suitable for large data sets. Finally, the experiments in this research show that our proposed models perform better than classical and alternative machine learning models for reject inference in credit scoring.

This paper considers improved forecasting in possibly nonlinear dynamic settings, with high-dimension predictors ("big data" environments). To overcome the curse of dimensionality and manage data and model complexity, we examine shrinkage estimation of a back-propagation algorithm of a deep neural net with skip-layer connections. We expressly include both linear and nonlinear components. This is a high-dimensional learning approach including both sparsity L1 and smoothness L2 penalties, allowing high-dimensionality and nonlinearity to be accommodated in one step. This approach selects significant predictors as well as the topology of the neural network. We estimate optimal values of shrinkage hyperparameters by incorporating a gradient-based optimization technique resulting in robust predictions with improved reproducibility. The latter has been an issue in some approaches. This is statistically interpretable and unravels some network structure, commonly left to a black box. An additional advantage is that the nonlinear part tends to get pruned if the underlying process is linear. In an application to forecasting equity returns, the proposed approach captures nonlinear dynamics between equities to enhance forecast performance. It offers an appreciable improvement over current univariate and multivariate models by RMSE and actual portfolio performance.

We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of technical trading strategies that can survive historical back-testing as well as form an overall aggregated portfolio trading strategy from the set of underlying trading strategies implemented on daily and intraday Johannesburg Stock Exchange data. The resulting population time-series are investigated using unsupervised learning for dimensionality reduction and visualisation. A key contribution is that the overall aggregated trading strategies are tested for statistical arbitrage using a novel hypothesis test proposed by Jarrow et al. on both daily sampled and intraday time-scales. The (low frequency) daily sampled strategies fail the arbitrage tests after costs, while the (high frequency) intraday sampled strategies are not falsified as statistical arbitrages after costs. The estimates of trading strategy success, cost of trading and slippage are considered along with an offline benchmark portfolio algorithm for performance comparison. In addition, the algorithms generalisation error is analysed by recovering a probability of back-test overfitting estimate using a nonparametric procedure introduced by Bailey et al.. The work aims to explore and better understand the interplay between different technical trading strategies from a data-informed perspective.

Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, Peng and Heyde (2013), and also data-based versions of loss-based risk measures introduced by Cont et al. (2013) and Sun et al. (2018).

We present a solution for the problems related to the application of multivariate Garch models to markets with a large number of stocks by restricting the form of the covariance matrix. It contains one component describing the market and a second simple component to account for the remaining contribution to the volatility. This allows the analytical calculation of the inverse covariance matrix. We compare our model with the results of other Garch models for the daily returns from the S&P500 market. The description of the covariance matrix turns out to be similar to the DCC model but has fewer free parameters and requires less computing time. The model also has the advantage that it contains the calculation of dynamic beta values. As applications we use the daily values of $\beta$ coefficients available from the market component to confirm a transition of the market in 2006. Further we discuss the relationship of our model with the leverage effect.

In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual banks before aggregation of their risks. In the present paper, we prove the dual representation of a particular subclass of such systemic risk measures and the existence and uniqueness of the optimal allocation related to them. We also introduce an associated utility maximization problem which has the same optimal solution as the systemic risk measure. In addition, the optimizer in the dual formulation provides a \textit{risk allocation} which is fair from the point of view of the individual financial institutions. The case with exponential utilities which allows for explicit computation is treated in details.

We consider the problem of super-replication (hedging without risk) for the Arbitrage Pricing Theory. The dual characterization of super-replication cost is provided. It is shown that the reservation prices of investors converge to this cost as their respective risk-aversion tends to infinity.

Manufacturing industry is heading towards socialization, interconnection, and platformization. Motivated by the infiltration of sharing economy usage in manufacturing, this paper addresses a new factory model -- shared factory -- and provides a theoretical architecture and some actual cases for manufacturing sharing. Concepts related to three kinds of shared factories which deal respectively with sharing production-orders, manufacturing-resources and manufacturing-capabilities, are defined accordingly. These three kinds of shared factory modes can be used for building correspondent sharing manufacturing ecosystems. On the basis of sharing economic analysis, we identify feasible key enabled technologies for configuring and running a shared factory. At the same time, opportunities and challenges of enabling the shared factory are also analyzed in detail. In fact, shared factory, as a new production node, enhances the sharing nature of social manufacturing paradigm, fits the needs of light assets and gives us a new chance to use socialized manufacturing resources. It can be drawn that implementing a shared factory would reach a win-win way through production value-added transformation and social innovation.

An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having a spatial extent, precisely such as environmental phenomena. The axiom of asymptotic spatial homogeneity is of particular interest since it allows one to quantify the rate of spatial diversification when the region under consideration becomes large. In this paper, we first investigate the general concepts of spatial risk measures and corresponding axioms further and thoroughly explain the usefulness of this theory for both actuarial science and practice. Second, in the case of a general cost field, we give sufficient conditions such that spatial risk measures associated with expectation, variance, Value-at-Risk as well as expected shortfall and induced by this cost field satisfy the axioms of asymptotic spatial homogeneity of order $0$, $-2$, $-1$ and $-1$, respectively. Last but not least, in the case where the cost field is a function of a max-stable random field, we provide conditions on both the function and the max-stable field ensuring the latter properties. Max-stable random fields are relevant when assessing the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of random fields. Overall, this paper improves our understanding of spatial risk measures as well as of their properties with respect to the space variable and generalizes many results obtained in Koch (2017).