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Found 10 papers, 5 papers with code
Signature Methods in Stochastic Portfolio Theory
We prove that these portfolios are universal in the sense that every continuous, possibly path-dependent, portfolio function of the market weights can be uniformly approximated by signature portfolios.
Global universal approximation of functional input maps on weighted spaces
This then applies in particular to approximation of (non-anticipative) path space functionals via functional input neural networks.
Joint calibration to SPX and VIX options with signature-based models
Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process.
Measure-valued processes for energy markets
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures.
Signature-based models: theory and calibration
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional continuous semimartingale.
Risk measures under model uncertainty: a Bayesian viewpoint
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property.
Expressive Power of Randomized Signature
We consider the question whether the time evolution of controlled differential equations on general state spaces can be arbitrarily well approximated by (regularized) regressions on features generated themselves through randomly chosen dynamical systems of moderately high dimension.
Discrete-time signatures and randomness in reservoir computing
A new explanation of geometric nature of the reservoir computing phenomenon is presented.
A generative adversarial network approach to calibration of local stochastic volatility models
We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface.
A new perspective on the fundamental theorem of asset pricing for large financial markets
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.
