5 citations · 15 across the 9 of their papers we have counts for
14 papers
Local signature-based expansions
Federico M. Bandi, Roberto Renò, Sara Svaluto-Ferro
We study the local (in time) expansion of a continuous-time process and its conditional moments, including the process' characteristic function. The expansions are conducted by usi…
Polynomial Volterra processes
Eduardo Abi Jaber, Christa Cuchiero, Luca Pelizzari +2
We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drif…
Signature SDEs from an affine and polynomial perspective
Christa Cuchiero, Sara Svaluto-Ferro, Josef Teichmann
Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their…
Joint calibration to SPX and VIX options with signature-based models
Christa Cuchiero, Guido Gazzani, Janka Möller +1
We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is sup…
Measure-valued processes for energy markets
Christa Cuchiero, Luca Di Persio, Francesco Guida +1
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the p…
Universal approximation theorems for continuous functions of càdlàg paths and Lévy-type signature models
Christa Cuchiero, Francesca Primavera, Sara Svaluto-Ferro
We prove a universal approximation theorem that allows to approximate continuous functionals of càdlàg (rough) paths uniformly in time and on compact sets of paths via linear funct…
Signature-based models: theory and calibration
Christa Cuchiero, Guido Gazzani, Sara Svaluto-Ferro
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-inf…
Measure-valued affine and polynomial diffusions
Christa Cuchiero, Francesco Guida, Luca di Persio +1
We introduce a class of measure-valued processes, which -- in analogy to their finite dimensional counterparts -- will be called measure-valued polynomial diffusions. We show the s…
Controlled Measure-Valued Martingales: a Viscosity Solution Approach
Alexander M. G. Cox, Sigrid Källblad, Martin Larsson +1
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, ca…
Propagation of minimality in the supercooled Stefan problem
Christa Cuchiero, Stefan Rigger, Sara Svaluto-Ferro
Supercooled Stefan problems describe the evolution of the boundary between the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing p…
Infinite dimensional polynomial processes
Christa Cuchiero, Sara Svaluto-Ferro
We introduce polynomial processes taking values in an arbitrary Banach space via their infinitesimal generator and the associated martingale problem. We obtain two represen…
Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces
Martin Larsson, Sara Svaluto-Ferro
We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other s…
Probability measure-valued polynomial diffusions
Christa Cuchiero, Martin Larsson, Sara Svaluto-Ferro
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of fi…
Polynomial jump-diffusions on the unit simplex
Christa Cuchiero, Martin Larsson, Sara Svaluto-Ferro
Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a ful…