• Corpus ID: 222140844

Abstract polynomial processes.

  title={Abstract polynomial processes.},
  author={Fred Espen Benth and Nils Detering and Paul Kruhner},
  journal={arXiv: Probability},
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, going far beyond Banach spaces. Moreover, we can be very flexible in the definition of what "polynomial" means. We show that "polynomial process" universally means "affine drift". Simple assumptions on the polynomial action operators lead to stronger characterisations on the polynomial class of processes. In our framework… 


Independent increment processes: a multilinearity preserving property
ABSTRACT We observe a multilinearity preserving property of conditional expectation for infinite-dimensional independent increment processes defined on some abstract Banach space B. It is similar in
Infinite-dimensional polynomial processes
We introduce polynomial processes taking values in an arbitrary Banach space B ${B}$ via their infinitesimal generator L $L$ and the associated martingale problem. We obtain two representations of
Multilinear processes in Banach space
A process (X(t))t≥0 taking values in R d is called a polynomial process if for every polynomial p of degree n on R, there exists another polynomial q of degree at most n such that E[p(X(t)) |Fs] =
Polynomial Processes for Power Prices
  • T. Ware
  • Mathematics
    Applied Mathematical Finance
  • 2019
ABSTRACT Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by
Probability measure-valued polynomial diffusions
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 finite dimensional
Lévy Processes in Lie Groups
It is well known that the distribution of a classical Levy process in a Euclidean space \(\mathbb {R}^d\) is determined by a triple of a drift vector, a covariance matrix, and a Levy measure, which
Polynomial processes and their applications to mathematical finance
We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains
Markov Cubature Rules for Polynomial Processes
Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial processes.
Limit Theorems for Stochastic Processes
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems
Polynomial diffusions and applications in finance
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest