相关论文: Projection of Functionals and Fast Pricing of Exot…

A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An…

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin…

In this work, we propose a new flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods…

We consider linearizations of stochastic differential equations with additive noise using the Karhunen-Lo\`eve expansion. We obtain our linearizations by truncating the expansion and writing the solution as a series of matrix-vector…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing…

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…

We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular…

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Lo\`eve (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed…

This paper makes two main contributions. First, we present a pedagogical review of the derivation of the three-term recurrence relation for Legendre polynomials, without relying on the classical Legendre differential equation, Rodrigues'…

We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…

Dupire's functional It\^o calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices. In this paper, we introduce a measure of…

In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to…

The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare…

Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…

Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general…