Related papers: A Reduced Basis Method for Parabolic Partial Diffe…
We investigate new developments of the combined Reduced-Basis and Empirical Interpolation Methods (RB-EIM) for parametrized nonlinear parabolic problems. In many situations, the cost of the EIM in the offline stage turns out to be…
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
A new approximate Bayesian inferential framework is proposed that exploits multiple information sources -- daily spot returns, high-frequency spot data and option prices -- and enables fast calculation of probabilistic predictions of future…
We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing…
In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified…
We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston…
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…
In this contribution, we introduce and numerically evaluate a certified and adaptive localized reduced basis method as a local model in a trust-region optimization method for parameter optimization constrained by partial differential…
In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navier-Stokes and Cahn-Hilliard problems. The full order finite…
We propose a novel structural estimation framework in which we train a surrogate of an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by…
This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and…
We examine the empirical performance of some parametric and nonparametric estimators of prices of options with a fixed time to maturity, focusing on variance-gamma and Heston models on one side, and on expansions in Hermite functions on the…
In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…
Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the…
We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…
We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the…
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…