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.

This paper analyses the Chinese Sovereign bond yield to find out the principal factors affecting the term structure of interest rate changes. We apply Principal Component Analysis (PCA) on our data consisting of the Chinese Sovereign bond from January 2002 till May 2018 with the different yield to maturity. Then we will discuss the multi-factor immunization model (method on hedging market risk) on a bond portfolio.

For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model in which portfolio optimization is usually done through dynamic programming. However, this assumes a known distribution for the parameters of the financial time series. We consider the situation where this distribution is unknown and needs to be estimated from the data that is arriving dynamically. We applied Bayesian filtering through dynamic linear models to sequentially update the parameters. We considered uncertain investment lifetime to make the model more adaptive to the market conditions. These updated parameters are put into the dynamic mean-variance problem to arrive at optimal efficient portfolios. Extensive simulations are conducted to study the effect of varying underlying parameters and investment horizon on the performance of the method. An implementation of this model to the S&P500 illustrates that the Bayesian updating is strongly favored by the data and that it is practically implementable.

The paper examines the potential of deep learning to support decisions in financial risk management. We develop a deep learning model for predicting whether individual spread traders secure profits from future trades. This task embodies typical modeling challenges faced in risk and behavior forecasting. Conventional machine learning requires data that is representative of the feature-target relationship and relies on the often costly development, maintenance, and revision of handcrafted features. Consequently, modeling highly variable, heterogeneous patterns such as trader behavior is challenging. Deep learning promises a remedy. Learning hierarchical distributed representations of the data in an automatic manner (e.g. risk taking behavior), it uncovers generative features that determine the target (e.g., trader's profitability), avoids manual feature engineering, and is more robust toward change (e.g. dynamic market conditions). The results of employing a deep network for operational risk forecasting confirm the feature learning capability of deep learning, provide guidance on designing a suitable network architecture and demonstrate the superiority of deep learning over machine learning and rule-based benchmarks.

We investigate the impact of available information on the estimation of the default probability within a generalized structural model for credit risk. The traditional structural model where default is triggered when the value of the firm's asset falls below a constant threshold is extended by relaxing the assumption of a constant default threshold. The default threshold at which the firm is liquidated is modeled as a random variable whose value is chosen by the management of the firm and dynamically adjusted to account for changes in the economy or the appointment of a new firm management. Investors on the market have no access to the value of the threshold and only anticipate the distribution of the threshold. We distinguish different information levels on the firm's assets and derive explicit formulas for the conditional default probability given these information levels. Numerical results indicate that the information level has a considerable impact on the estimation of the default probability and the associated credit yield spread.

This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information.

For estimating the hidden drift it is crucial to consider the conditional distribution of the drift given the available observations, the so-called filter. For an investor observing both the return process and the discrete-time expert opinions, we investigate in detail the asymptotic behavior of the filter as the frequency of the arrival of expert opinions tends to infinity. In our setting, a higher frequency of expert opinions comes at the cost of accuracy, meaning that as the frequency of expert opinions increases, the variance of expert opinions becomes larger. We consider a model where information dates are deterministic and equidistant and another model where the information dates arrive randomly as the jump times of a Poisson process. In both cases we derive limit theorems stating that the information obtained from observing the discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process which can be interpreted as a continuous-time expert.

We use our limit theorems to derive so-called diffusion approximations of the filter for high-frequency discrete-time expert opinions. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

While time series momentum is a well-studied phenomenon in finance, common strategies require the explicit definition of both a trend estimator and a position sizing rule. In this paper, we introduce Deep Momentum Networks -- a hybrid approach which injects deep learning based trading rules into the volatility scaling framework of time series momentum. The model also simultaneously learns both trend estimation and position sizing in a data-driven manner, with networks directly trained by optimising the Sharpe ratio of the signal. Backtesting on a portfolio of 88 continuous futures contracts, we demonstrate that the Sharpe-optimised LSTM improved traditional methods by more than two times in the absence of transactions costs, and continue outperforming when considering transaction costs up to 2-3 basis points. To account for more illiquid assets, we also propose a turnover regularisation term which trains the network to factor in costs at run-time.

We discuss the objectives of automation equipped with non-trivial decision making, or creating artificial intelligence, in the financial markets and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant. For this unintentional yet welcome aftereffect to set in a foundational list of guiding principles needs to be present. A consideration of these requirements allows us to propose a test of intelligence for trading programs, on the lines of the Turing Test, long the benchmark for intelligent machines. We discuss the application of this methodology to the dilemma in finance, which is whether, when and how much to Buy, Sell or Hold.

As impressively shown by the financial crisis in 2007/08, contagion effects in financial networks harbor a great threat for the stability of the entire system. Without sufficient capital requirements for banks and other financial institutions, shocks that are locally confined at first can spread through the entire system and be significantly amplified by various contagion channels. The aim of this thesis is thus to investigate in detail two selected contagion channels of this so-called systemic risk, provide mathematical models and derive consequences for the systemic risk management of financial institutions. The first contagion channel we consider is default contagion. The underlying effect is here that insolvent institutions cannot service their debt or other financial obligations anymore - at least partially. Debtors and other directly impacted parties in the system are thus forced to write off their losses and can possibly be driven into insolvency themselves due to their incurred financial losses. This on the other hand starts a new round in the default contagion process. In our model we simplistically describe each institution by all the financial positions it is exposed to as well as its initial capital. In doing so, our starting point is the work of Detering et al. (2017) - a model for contagion in unweighted networks - which particularly considers the exact network configuration to be random and derives asymptotic results for large networks. We extend this model such that weighted networks can be considered and an application to financial networks becomes possible. More precisely, for any given initial shock we deduce an explicit asymptotic expression for the total damage caused in the system by contagion and provide a necessary and sufficient criterion for an unshocked financial system to be stable against small shocks. Moreover, ...

Recent technology advances have enabled firms to flexibly process and analyze sophisticated employee performance data at a reduced and yet significant cost. We develop a theory of optimal incentive contracting where the monitoring technology that governs the above procedure is part of the designer's strategic planning. In otherwise standard principal-agent models with moral hazard, we allow the principal to partition agents' performance data into any finite categories and to pay for the amount of information the output signal carries. Through analysis of the trade-off between giving incentives to agents and saving the monitoring cost, we obtain characterizations of optimal monitoring technologies such as information aggregation, strict MLRP, likelihood ratio-convex performance classification, group evaluation in response to rising monitoring costs, and assessing multiple task performances according to agents' endogenous tendencies to shirk. We examine the implications of these results for workforce management and firms' internal organizations.

This paper introduces a search problem where a consumer has to first become aware of an alternative, before being able to search it. Initially, the consumer is aware of only a few alternatives. During search, the consumer sequentially decides between searching alternatives he is already aware of and expanding awareness to discover more products. I show that the optimal policy for this search problem is fully characterized by simple reservation values. Moreover, I prove that the purchase outcome of a consumer optimally solving the search problem is equivalent to the consumer simply choosing the product offering the largest value on a predetermined index.

We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor's risk preference, but learns it over time by observing her portfolio choices in different market environments. We develop an exploration-exploitation algorithm which trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor's risk aversion. We show that the algorithm's value function converges to the optimal value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor's mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor's opportunity cost for making portfolio decisions.

The possibility of re-switching of techniques in Piero Sraffa's intersectoral model, namely the returning capital-intensive techniques with monotonic changes in the profit rate, is traditionally considered as a paradox putting at stake the viability of the neoclassical theory of production. It is argued here that this phenomenon can be rationalized within the neoclassical paradigm. Sectoral interdependencies can give rise to non-monotonic effects of progressive variations in income distribution on relative prices. The re-switching of techniques is, therefore, the result of cost-minimizing technical choices facing returning ranks of relative input prices in full consistency with the neoclassical perspective.

In this paper we study the impact of errors in wind and solar power forecasts on intraday electricity prices. We develop a novel econometric model which is based on day-ahead wholesale auction curves data and errors in wind and solar power forecasts. The model shifts day-ahead supply curves to calculate intraday prices. We apply our model to the German EPEX SPOT SE data. Our model outperforms both linear and non-linear benchmarks. Our study allows us to conclude that errors in renewable energy forecasts exert a non-linear impact on intraday prices. We demonstrate that additional wind and solar power capacities induce non-linear changes in the intraday price volatility. Finally, we comment on economical and policy implications of our findings.

We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transform of general Gaussian processes in terms of Fredholm's determinant and resolvent. Furthermore , we link the characteristic exponents to a system of non-standard infinite dimensional matrix Riccati equations. This leads to a second representation of the Laplace transform for a special case of convolution kernel. In practice, we show that both representations can be approximated by either closed form solutions of conventional Wishart distributions or finite dimensional matrix Riccati equations stemming from conventional linear-quadratic models. This allows fast pricing in a variety of highly flexible models, ranging from bond pricing in quadratic short rate models with rich autocorrelation structures, long range dependence and possible default risk, to pricing basket options with covariance risk in multivariate rough volatility models.

We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this method from a numerical standpoint and investigated the accuracy of integration formulas based on the Monte-Carlo methodology: quantitative error bounds were discussed and, in this short note, we outline the main ideas of our approach. The techniques of transportation and reproducing kernels lead us to a very efficient methodology for numerical simulations in many practical applications, and provide some light on the methods used by the artificial intelligence community. For applications in the finance industry, our method allows us to compute many types of risk measures with an accurate and fast algorithm. We propose theoretical arguments as well as extensive numerical tests in order to justify sharp convergence rates, leading to rather optimal computational times. Cases of direct interest in finance support our claims and the importance of the problem of the curse of dimensionality in finance applications is briefly discussed.