5 citations · 22 across the 15 of their papers we have counts for
20 papers
Polynomial McKean-Vlasov SDEs
Christa Cuchiero, Janka Möller
We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drif…
Polynomial interacting particle systems and non-linear SPDEs for market capitalization curves
Christa Cuchiero, Florian Huber
Motivated by the robustness of the capital distribution curves, we study the behavior of a certain polynomial equity market model as the number of companies goes to infinity. More…
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 Methods in Stochastic Portfolio Theory
Christa Cuchiero, Janka Möller
In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by…
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…
Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups
Christa Cuchiero, Christoph Reisinger, Stefan Rigger
We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proo…
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…
Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem
Christa Cuchiero, Christoph Reisinger, Stefan Rigger
We consider the problem faced by a central bank which bails out distressed financial institutions that pose systemic risk to the banking sector. In a structural default model with…
Model-free Portfolio Theory: A Rough Path Approach
Andrew L. Allan, Christa Cuchiero, Chong Liu +1
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compare…
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…
A weak solution theory for stochastic Volterra equations of convolution type
Eduardo Abi Jaber, Christa Cuchiero, Martin Larsson +1
We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients an…
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 processes in stochastic portfolio theory
Christa Cuchiero
We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding…
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…
Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio
Christa Cuchiero, Walter Schachermayer, Ting-Kam Leonard Wong
Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant re…