Related papers: Functional central limit theorems for rough volati…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the…
This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a…
Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
In this article, we propose a MUSCL-Hancock-type second-order scheme for the discretization of a general class of non-local conservation laws and present its convergence analysis. The main difficulty in designing a MUSCL-Hancock-type scheme…
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use…
Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under…
The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…
The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the…