Markov Cubature Rules for Polynomial Processes

@article{Filipovic2020MarkovCR,
  title={Markov Cubature Rules for Polynomial Processes},
  author={Damir Filipovi'c and Martin Larsson and Sergio Pulido},
  journal={ERN: Other Econometrics: Econometric \& Statistical Methods (Topic)},
  year={2020}
}
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study such rules using algebraic techniques. Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial… 
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References

SHOWING 1-10 OF 42 REFERENCES
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…
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…
Cubature on Wiener space in infinite dimension
  • C. Bayer, J. Teichmann
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
We prove a stochastic Taylor expansion for stochastic partial differential equations (SPDEs) and apply this result to obtain cubature methods, i.e. high-order weak approximation schemes for SPDEs, in…
A DIFFUSION LIMIT FOR GENERALIZED CORRELATED RANDOM WALKS
A generalized correlated random walk is a process of partial sums Xk = k P j=1 Y j such that (X;Y ) forms a Markov chain. For a sequence (X n ) of such processes where each Y n j takes only two…
The Jacobi stochastic volatility model
TLDR
A novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process is introduced and the Heston model is included as a limit case.
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…
Numerical Methods for Stochastic Control Problems in Continuous Time
A powerful and usable class of methods for numerically approximating the solutions to optimal stochastic control problems for diffusion, reflected diffusion, or jump-diffusion models is discussed.…
Cubature methods for stochastic (partial) differential equations in weighted spaces
The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded test functions. We first describe a…
Polynomial Diffusion Models for Life Insurance Liabilities
Approximation and Weak Convergence Methods for Random Processes
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and…
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