arXiv research

Study on PDEs in Heston model with unique solution and convergence proof.

The paper generalizes Feynman-Kac formula for volatility uncertainty.

Three theorems about arbitrage bubbles in financial equations.

At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratings on which prices are influenced by additional factors and rating, and behavior of this system is described by SDE driven by Wiener process…

This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators…

ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the Feynman-Kac theorem which is easily applicable only when r is bounded from below. Sec…

We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, althou…

In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral …

New methods solve SPDEs for financial derivative pricing.

FKEE estimates expectations without samples, using diffusion bridges and PINNs.

New method recovers BSDE from financial data without ergodicity.

We prove a Feynman-Kac formula for differential forms satisfying absolute boundary conditions on Riemannian manifolds with boundary and of bounded geometry. We use this to construct $L^2$ harmonic forms out of bounded ones on the universal cover of a compact Riemannian manifold whose geometry displays a positivity prop…

The paper develops a Feynman-Kac formula for perturbations of order ≤ 1 in noncommutative geometry.

AFT combines AIS, SMC, and NFs for better Monte Carlo estimates.

Functional-analytic method for stochastic parallel transport in bundles.

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous mode…

New method trains partial Bayesian neural networks efficiently.

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…

New method steers protein design towards desired properties.

Unified kernel framework extends to stochastic systems, improving numerical stability.

Study analyzes derivative-free loss method for solving PDEs and fluid problems.

This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod topology, which reveals the intrinsic connection between overfitting Dirichlet …

We use tools from $n$-dimensional Brownian motion in conjunction with the Feynman-Kac formulation of heat diffusion to study nodal geometry on a compact Riemannian manifold $M$. On one hand we extend a theorem of Lieb and prove that any nodal domain $Ω_λ$ almost fully contains a ball of radius $\sim \frac{1}{\sqrtλ}$. …

Improved diffusion models using energy distillation and sequential Monte Carlo.

Exchange uses incentives to optimize limit order book dynamics.

Paper improves robustness and sparsity in adversarially trained DNNs.

We develop a new model for VIX derivatives with closed-form solutions.

In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility funct…

We prove existence, regularity and a Feynman-Kač representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian option with arithmetic average.

Study heat profiles and eigenfunctions using Brownian motion.

Study of mean curvature flows with conical singularities using mathematical techniques.

Study an index theorem on manifolds with S^1 action using heat kernels and orbifolds.

The paper develops methods to price and hedge options in path-dependent stock models.

Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fix…

Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.

New method improves training of PINNs for PDEs by adding noisy supervision terms.

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally Hölder continuous with exponent $δ\in (0, 1]$, the stochastic solution, which represents the price of a European option, is show…

Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.

This paper models short rates with jumps using PDEs.

Deep learning solves high-dimensional PDEs efficiently.

The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…

This study quantifies systemic importance in global banks using a continuous framework that amplifies localized shocks.

Study indifference pricing for insurance policies in a regime-switching market model.

We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as ass…

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexi…

Deep density methods improve filtering in high-dimensional systems.