Polynomial jump-diffusion models

D Filipović, M Larsson - Stochastic Systems, 2020 - pubsonline.informs.org
We develop a comprehensive mathematical framework for polynomial jump diffusions in a
semimartingale context, which nest affine jump diffusions and have broad applications in …

[HTML][HTML] Polynomial processes in stochastic portfolio theory

C Cuchiero - Stochastic processes and their applications, 2019 - Elsevier
We introduce polynomial processes in the context of stochastic portfolio theory to model
simultaneously companies' market capitalizations and the corresponding market weights …

[HTML][HTML] Measure-valued affine and polynomial diffusions

C Cuchiero, L Di Persio, F Guida… - Stochastic Processes and …, 2024 - Elsevier
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 …

Polynomial Volterra processes

EA Jaber, C Cuchiero, L Pelizzari, S Pulido… - arXiv preprint arXiv …, 2024 - arxiv.org
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 …

Infinite-dimensional polynomial processes

C Cuchiero, S Svaluto-Ferro - Finance and Stochastics, 2021 - Springer
We introduce polynomial processes taking values in an arbitrary Banach space BB via their
infinitesimal generator LL and the associated martingale problem. We obtain two …

Polynomial jump-diffusions on the unit simplex

C Cuchiero, M Larsson, S Svaluto-Ferro - 2018 - projecteuclid.org
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 …

A multifactor polynomial framework for long-term electricity forwards with delivery period

X Kleisinger-Yu, V Komaric, M Larsson… - SIAM Journal on Financial …, 2020 - SIAM
We propose a multifactor polynomial framework to model and hedge long-term electricity
contracts with delivery period. This framework has several advantages: the computation of …

Polynomial Volterra processes

E Abi Jaber, C Cuchiero, L Pelizzari, S Pulido… - 2024 - hal.science
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 …

Reduced-form framework under model uncertainty

F Biagini, Y Zhang - 2019 - projecteuclid.org
In this paper, we introduce a sublinear conditional expectation with respect to a family of
possibly nondominated probability measures on a progressively enlarged filtration. In this …

Abstract polynomial processes

FE Benth, N Detering, P Kruhner - arXiv preprint arXiv:2010.02483, 2020 - arxiv.org
We suggest a novel approach to polynomial processes solely based on a polynomial action
operator. With this approach, we can analyse such processes on general state spaces …