Related papers: Operator splitting schemes for the two-asset Merto…
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
Machine learning for partial differential equations (PDEs) is a hot topic. In this paper we introduce and analyse a Deep BSDE scheme for nonlinear integro-PDEs with unbounded nonlocal operators -problems arising in e.g. stochastic control…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
A novel approach to Riemann--Hilbert problems of particular class is introduced. The approach is applicable to problems in which the multiplicative jump is set on a half-line. Such problems are linked to some Wiener--Hopf problems motivated…
In this paper, our focus lies on the Merton's jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of…
The port-Hamiltonian approach presents an energy-based modeling of dynamical systems with energy-conservative and energy-dissipative parts as well as an interconnection over the so-called ports. In this paper, we apply an operator splitting…
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient…
We describe two separate wavelength discretization schemes that can be used in the numerical solution of the comoving frame radiative transfer equation. We present an improved second order discretization scheme and show that it leads to…
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium…
By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent…
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding…
The present article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under…