相关论文: Pricing double barrier options on homogeneous diff…

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…

We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…

In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes…

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…

Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as…

This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…

We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for…

Nowadays, with the availability of massive amount of trade data collected, the dynamics of the financial markets pose both a challenge and an opportunity for high frequency traders. In order to take advantage of the rapid, subtle movement…

In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction…

We consider an important class of derivative contracts written on multiple assets (so-called spread options) which are traded on a wide range of financial markets. The present paper introduces a new approximation method of density functions…

We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenisation theory provides a coarse-grained…

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…

We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…

Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…

We propose a generalization of the Bass diffusion model in discrete-time that explicitly models the effect of price in adoption. Our model is different from earlier price-incorporated models and fits well to adoption data for various…

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…

In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by…

We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function…

We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…