Related papers: Multivariate transient price impact and matrix-val…
Decay rates for the sequence of eigenvalues of positive and compact integral operators has been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square…
The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of…
We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific…
The purpose of this paper is to investigate the distribution of zeros of entire functions which can be represented as the Fourier transforms of certain admissible kernels. The principal results bring to light the intimate connection between…
Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution…
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
We compare the predictions of the stationary Kyle model, a microfounded multi-step linear price impact model in which market prices forecast fundamentals through information encoded in the order flow, with those of the propagator model, a…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…
In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly…
The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we…
Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined…