相关论文: Approximation and regularity results for the Hesto…

Our main objective in this paper is to develop a second-order stochastic numerical method which generalizes the well-known deterministic TR-BDF2 scheme. Since most stochastic techniques used for approximating the solution of a stochastic…

We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…

We study the weak convergence order of two Euler-type discretizations of the log-Heston Model where we use symmetrization and absorption, respectively, to prevent the discretization of the underlying CIR process from becoming negative. If…

We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…

For valuing European options, a straightforward model is the well-known Black-Scholes formula. Contrary to market reality, this model assumed that interest rate and volatility are constant. To modify the Black-Scholes model, Heston and…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear…

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…

This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

We establish the existence of solutions to common noise McKean-Vlasov martingale problems for coefficients with low regularity. Our approach is able to handle the key challenge posed by drift coefficients that are discontinuous with respect…

This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…

We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…

We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility…

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…

We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…

We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index $H \in (-1/2,1/2)$, we derive a…