2,746 research outputs found

    Quantifying Equity Risk Premia: Financial Economic Theory and High-Dimensional Statistical Methods

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    The overarching question of this dissertation is how to quantify the unobservable risk premium of a stock when its return distribution varies over time. The first chapter, titled “Theory-based versus machine learning-implied stock risk premia”, starts with a comparison of two competing strands of the literature. The approach advocated by Martin and Wagner (2019) relies on financial economic theory to derive a closed-form approximation of conditional risk premia using information embedded in the prices of European options. The other approach, exemplified by the study of Gu et al. (2020), draws on the flexibility of machine learning methods and vast amounts of historical data to determine the unknown functional form. The goal of this study is to determine which of the two approaches produces more accurate measurements of stock risk premia. In addition, we present a novel hybrid approach that employs machine learning to overcome the approximation errors induced by the theory-based approach. We find that our hybrid approach is competitive especially at longer investment horizons. The second chapter, titled “The uncertainty principle in asset pricing”, introduces a representation of the conditional capital asset pricing model (CAPM) in which the betas and the equity premium are jointly characterized by the information embedded in option prices. A unique feature of our model is that its implied components represent valid measurements of their physical counterparts without the need for any further risk adjustment. Moreover, because the model’s time-varying parameters are directly observable, the model can be tested without any of the complications that typically arise from statistical estimation. One of the main empirical findings is that the well-known flat relationship between average predicted and realized excess returns of beta-sorted portfolios can be explained by the uncertainty governing market excess returns. In the third chapter, titled “Multi-task learning in cross-sectional regressions”, we challenge the way in which cross-sectional regressions are used to test factor models with time-varying loadings. More specifically, we extend the procedure by Fama and MacBeth (1973) by systematically selecting stock characteristics using a combination of l1- and l2-regularization, known as the multi-task Lasso, and addressing the bias that is induced by selection via repeated sample splitting. In the empirical part of this chapter, we apply our testing procedure to the option-implied CAPM from chapter two, and find that, while variants of the momentum effect lead to a rejection of the model, the implied beta is by far the most important predictor of cross-sectional return variation

    Twelve times faster yet accurate: a new state‐of‐the‐art in radiation schemes via performance and spectral optimization

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    Radiation schemes are critical components of Earth system models that need to be both efficient and accurate. Despite the use of approximations such as 1D radiative transfer, radiation can account for a large share of the runtime of expensive climate simulations. Here we seek a new state‐of‐the‐art in speed and accuracy by combining code optimization with improved algorithms. To fully benefit from new spectrally reduced gas optics schemes, we restructure code to avoid short vectorized loops where possible by collapsing the spectral and vertical dimensions. Our main focus is the ecRad radiation scheme, where this requires batching of adjacent cloudy layers, trading some simplicity for improved vectorization and instruction‐level parallelism. When combined with common optimization techniques for serial code and porting widely used two‐stream kernels fully to single precision, we find that ecRad with the TripleClouds solver becomes 12 times faster than the operational radiation scheme in ECMWF's Integrated Forecast System (IFS) cycle 47r3, which uses a less accurate gas optics model (RRMTG) and a more noisy solver (McICA). After applying the spectral reduction and extensive optimizations to the more sophisticated SPARTACUS solver, we find that it’s 2.5 times faster than IFS cy47r3 radiation, making cloud 3D radiative effects affordable to compute in large‐scale models. The code optimization itself gave a threefold speedup for both solvers. While SPARTACUS is still under development, preliminary experiments show slightly improved medium‐range forecasts of 2‐m temperature in the tropics, and in year‐long coupled atmosphere‐ocean simulations the 3D effects warm the surface substantially

    Backpropagation Beyond the Gradient

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    Automatic differentiation is a key enabler of deep learning: previously, practitioners were limited to models for which they could manually compute derivatives. Now, they can create sophisticated models with almost no restrictions and train them using first-order, i. e. gradient, information. Popular libraries like PyTorch and TensorFlow compute this gradient efficiently, automatically, and conveniently with a single line of code. Under the hood, reverse-mode automatic differentiation, or gradient backpropagation, powers the gradient computation in these libraries. Their entire design centers around gradient backpropagation. These frameworks are specialized around one specific task—computing the average gradient in a mini-batch. This specialization often complicates the extraction of other information like higher-order statistical moments of the gradient, or higher-order derivatives like the Hessian. It limits practitioners and researchers to methods that rely on the gradient. Arguably, this hampers the field from exploring the potential of higher-order information and there is evidence that focusing solely on the gradient has not lead to significant recent advances in deep learning optimization. To advance algorithmic research and inspire novel ideas, information beyond the batch-averaged gradient must be made available at the same level of computational efficiency, automation, and convenience. This thesis presents approaches to simplify experimentation with rich information beyond the gradient by making it more readily accessible. We present an implementation of these ideas as an extension to the backpropagation procedure in PyTorch. Using this newly accessible information, we demonstrate possible use cases by (i) showing how it can inform our understanding of neural network training by building a diagnostic tool, and (ii) enabling novel methods to efficiently compute and approximate curvature information. First, we extend gradient backpropagation for sequential feedforward models to Hessian backpropagation which enables computing approximate per-layer curvature. This perspective unifies recently proposed block- diagonal curvature approximations. Like gradient backpropagation, the computation of these second-order derivatives is modular, and therefore simple to automate and extend to new operations. Based on the insight that rich information beyond the gradient can be computed efficiently and at the same time, we extend the backpropagation in PyTorch with the BackPACK library. It provides efficient and convenient access to statistical moments of the gradient and approximate curvature information, often at a small overhead compared to computing just the gradient. Next, we showcase the utility of such information to better understand neural network training. We build the Cockpit library that visualizes what is happening inside the model during training through various instruments that rely on BackPACK’s statistics. We show how Cockpit provides a meaningful statistical summary report to the deep learning engineer to identify bugs in their machine learning pipeline, guide hyperparameter tuning, and study deep learning phenomena. Finally, we use BackPACK’s extended automatic differentiation functionality to develop ViViT, an approach to efficiently compute curvature information, in particular curvature noise. It uses the low-rank structure of the generalized Gauss-Newton approximation to the Hessian and addresses shortcomings in existing curvature approximations. Through monitoring curvature noise, we demonstrate how ViViT’s information helps in understanding challenges to make second-order optimization methods work in practice. This work develops new tools to experiment more easily with higher-order information in complex deep learning models. These tools have impacted works on Bayesian applications with Laplace approximations, out-of-distribution generalization, differential privacy, and the design of automatic differentia- tion systems. They constitute one important step towards developing and establishing more efficient deep learning algorithms

    Search and Explore: Symbiotic Policy Synthesis in POMDPs

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    This paper marries two state-of-the-art controller synthesis methods for partially observable Markov decision processes (POMDPs), a prominent model in sequential decision making under uncertainty. A central issue is to find a POMDP controller - that solely decides based on the observations seen so far - to achieve a total expected reward objective. As finding optimal controllers is undecidable, we concentrate on synthesising good finite-state controllers (FSCs). We do so by tightly integrating two modern, orthogonal methods for POMDP controller synthesis: a belief-based and an inductive approach. The former method obtains an FSC from a finite fragment of the so-called belief MDP, an MDP that keeps track of the probabilities of equally observable POMDP states. The latter is an inductive search technique over a set of FSCs, e.g., controllers with a fixed memory size. The key result of this paper is a symbiotic anytime algorithm that tightly integrates both approaches such that each profits from the controllers constructed by the other. Experimental results indicate a substantial improvement in the value of the controllers while significantly reducing the synthesis time and memory footprint.Comment: Accepted to CAV 202

    A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation

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    Over the last two decades, the hierarchical equations of motion (HEOM) of Tanimura and Kubo have become the equation of motion-based tool for numerically exact calculations of system-bath problems. The HEOM is today generalized to many cases of dissipation and transfer processes through an external bath. In spatially extended photonic systems, the propagation of photons through the bath leads to retardation/delays in the coupling of quantum emitters. Here, the idea behind the HEOM derivation is generalized to the case of photon retardation and applied to the simple example of two dielectric slabs. The derived equations provide a simple reliable framework for describing retardation and may provide an alternative to path integral treatments

    Exploring the calibration of cosmological probes used in gravitational-wave and multi-messenger astronomy

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    The field of gravitational wave astronomy has grown remarkably since the first direct detection of gravitational waves on 14th September 2015. The signal, originating from the merger of two black holes, was detected by the two US-based Advanced LIGO interferometers in Hanford (Washington State) and Livingston (Louisiana). The second observing run of the Advanced LIGO and Virgo detectors marked the first detection of a binary neutron star merger, along with its electromagnetic counterparts. The optical follow-up of the merger led to the first confirmed observations of a kilonova, an electromagnetic counterpart to binary neutron star and neutron star-black hole mergers whose existence was first predicted in 1970s. Following the multimessenger observations of the binary neutron star merger GW170817, constraints were put on the rate of expansion of the Universe using both gravitational wave and electromagnetic data. These measurements could help us understand the current tension between early-Universe and late-Universe measurements of the Hubble constant H0. The use of gravitational wave signals for measuring the rate of expansion of the Universe was proposed by Schutz in 1986. Compact binary coalescences can be used as distance markers, a gravitational wave analogue to standard candles: "Standard Sirens". Measurements of the Hubble constant from standard sirens are independent from previous methods of constraining H0. Bright sirens are gravitational wave signals that are detected coincidentally with electromagnetic signatures. These "bright" gravitational wave sirens are powerful cosmological probes, allowing us to extract information on both the distance and the redshift of the source. It is therefore important to maximise these coincident detections, and to carefully calibrate the data extracted from any standard siren. The work presented in this thesis can be divided into three main topics, all under the umbrella of maximising scientific returns from observations of compact binary coalescences. These three topics are: kilonova parameter estimation, cosmology with gravitational waves, and calibration of advanced gravitational wave detectors. We present work on inferring parameters from kilonova light curves. Ejecta parameters and information about the merging time of the progenitor is extracted from simulated kilonova light curves. We explore the consequence of neglecting some aspects of microphysics on the resulting parameter estimation. We also present new results on the inference of the Hubble constant through the application of a robust test of galaxy catalogue completeness to the current gravitational wave cosmology pipeline. We explore the impact of adopting a robust estimate of the apparent magnitude threshold mthr for the galaxy catalogues used in gravitational wave cosmology on the final inference of the Hubble constant H0 from standard sirens, and compare the results to those obtained when adopting a conservative estimate for mthr. Finally, we present the first results from the prototype of a Newtonian Calibrator at the LIGO Hanford detector. Calibrating the LIGO detectors is crucial to the extraction of the gravitational wave source parameters that are used in cosmology with standard sirens

    Open problems in deformations of Artinian algebras, Hilbert schemes and around

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    We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that emerge from applications. In view of many advances in recent years, we can hope that all of them are in the range of current methods

    Serial-batch scheduling – the special case of laser-cutting machines

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    The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

    A multifluid model with chemically reacting components -- construction of weak solutions

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    We investigate the existence of weak solutions to the multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of the irreversible chemical reaction and assume the nonlinear relation between the pressure and the particular densities. These assumptions cause additional difficulties in the mathematical analysis, due to the possible presence of vacuum. It is shown that there exists a global weak solution, satisfying the LL^\infty bounds for all the components. Moreover, despite the lack of regularity on the gradients, we obtain strong compactness of densities in LpL^p spaces. The applied method captures the properties of the models of high generality, which admit an arbitrary number of components. Furthermore, the framework we develop can handle models that contain both diffusing and non-diffusing elements

    Scalable Quantum Computation of Highly Excited Eigenstates with Spectral Transforms

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    We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational manner. This is enabled by the efficient computation of inverse expectation values, taking advantage of the QLSP solvers' exponentially better scaling in problem size without concealing exponentially costly pre/post-processing steps that usually accompanies it. We detail implementations of this scheme for both fault-tolerant and near-term quantum computers, analyse their efficiency and implementability, and discuss applications and simulation results in many-body physics and quantum chemistry that demonstrate its superior effectiveness and scalability over existing approaches.Comment: 16 pages, 6 figure
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