Related papers: Variance optimal hedging for continuous time addit…

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration…

The framework of differential inclusions encompasses modern optimal control and the calculus of variations. Necessary optimality conditions in the literature identify potentially optimal paths, but do not show how to perturb paths to…

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.

A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to…

In this paper we formulate a regression problem to predict realized volatility by using option price data and enhance VIX-styled volatility indices' predictability and liquidity. We test algorithms including regularized regression and…

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution.…

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real-…

We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted…

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to…

Fermionic Monte Carlo calculations with continuous auxiliary fields often encounter infinite variance problem from fermionic observables. This issue renders the estimation of observables unreliable, even with an infinite number of samples.…

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a…

By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…

We construct an aggregator for a family of Snell envelopes in a nondominated framework. We apply this construction to establish a robust hedging duality, along with the existence of a minimal hedging strategy, in a general semi-martingale…

Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a…