Publications related to Classical orthogonal polynomials

Option pricing with orthogonal polynomial expansions

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial ...

WILEY2019

A New Approach For American Option Pricing: The Dynamic Chebyshev Method

Kathrin Beatrice Glau

We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is that it allows us ...

SIAM PUBLICATIONS2019

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Florian Karl Richter

A set

R\subset \mathbb{N}

is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every

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there exists a set

B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}

, where $a_{1},\ldots ,a_ ...

2019

Distributed Signal Processing via Chebyshev Polynomial Approximation

Pascal Frossard, Pierre Vandergheynst, Daniel Kressner, David Shuman

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of ...

2018

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

Daniel Kuhn, Grani Adiwena Hanasusanto

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust ...

2018

Momentum-space conformal blocks on the light cone

Marc Gillioz

We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in ...

SPRINGER2018

Arithmetic and metric aspects of open de Rham spaces

Dimitri Stelio Wyss, Tamás Hausel, Michael Lennox Wong

In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivia ...

2018

Verification and validation procedures with applications to plasma-edge turbulence simulations

Fabio Riva

Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynam ...

EPFL2017

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

Paolo Ricci, Fabio Riva

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the mod ...

American Institute of Physics2017

Classical orthogonal polynomials

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Option pricing with orthogonal polynomial expansions

A New Approach For American Option Pricing: The Dynamic Chebyshev Method

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Distributed Signal Processing via Chebyshev Polynomial Approximation

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

Momentum-space conformal blocks on the light cone

Arithmetic and metric aspects of open de Rham spaces

Verification and validation procedures with applications to plasma-edge turbulence simulations

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Distributed Signal Processing via Chebyshev Polynomial Approximation

Momentum-space conformal blocks on the light cone

A New Approach For American Option Pricing: The Dynamic Chebyshev Method

Arithmetic and metric aspects of open de Rham spaces

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

Verification and validation procedures with applications to plasma-edge turbulence simulations

Option pricing with orthogonal polynomial expansions

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls