A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Method uses neural networks to fit nonlinear operators from data.
The paper develops and tests operator splitting schemes for American options in a complex model.
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential, integro-differential, and fractional order operators. Here, Gaussian process priors are modifie…
The paper efficiently solves a complex option valuation equation for two assets.
Study deep neural nets for solving complex insurance equations.
A second order linear integro-differential equation with Volterra integral operator and strong singularities at the endpoints (zero and infinity) is considered. Under limit conditions at the singular points, and some natural assumptions, the problem is a singular initial problem with limit normalizing conditions at inf…
We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution …
Simplified calculus for stochastic processes simplifies complex financial calculations.
Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function in the gap [0,1], is characterized by . This conjecture can be understood as a consequence of 1/2-order fractional differential chara…
An unsupervised deep learning method solves PIDEs for option pricing.
New deep learning method for option pricing in jump-diffusion models.
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference di…
Physics-informed neural networks approximate diffusion process pdfs efficiently.
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…
This work integrates differentiation and integration in Physics-Informed Neural Networks.
Study geometric step options with jumps, deriving pricing equations and characterizations.
In this article, a three-time levels compact scheme is proposed to solve the partial integro-differential equation governing the option prices under jump-diffusion models. In the proposed compact scheme, the second derivative approximation of unknowns is approximated by the value of unknowns and their first derivative …
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the…
Study of financial models using PIDEs with and without market liquidity.
Isogeometric analysis simplifies option pricing with NURBS surfaces.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
Mean-field approximations simplify insurance liability calculations.
New model for electricity pricing captures mean reversion and jumps.
A new method calibrates jump-diffusion models from option prices.
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
We consider an integro-differential equation derived from a system of coupled parabolic PDE and an ODE which describes an European option pricing with liquidity shocks. We study the well-posedness and prove comparison principle for the corresponding initial value problem.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
The paper studies value adjustments and dynamic hedging for reinsurance counterparty risk.
We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected terminal utility of his wealth. We assume a mean-reverting additive process to drive t…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a jump-diffusion model where the jump component consists of a Levy process of compound Poisson …
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…
New method infers hidden states in continuous-time phenomena better than traditional models.
We analyze deep neural networks in the large size and iteration limit, revealing a deterministic system of equations.
The paper solves an insurance problem using mean-variance and rank-dependent utility theory.
Generalizes Hasimoto transformation to arbitrary flows on space curves.
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Lévy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness a…
Develops a PIDE framework for option pricing with stochastic volatility and jumps.
This paper develops a novel numerical method for pricing American options in a two-asset jump-diffusion model.
We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. A uniqueness theorem is given for the solutions of this equation. This result generalizes Dupire…
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equati…
New methods for uncertainty in neural networks with leaky ReLU activations.
Develops a PD estimation model using Lévy-driven processes for credit risk.
We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbit…
Paper proves existence and uniqueness of solutions to PIDEs in Bessel spaces for option pricing.
We model the term structure of the forward default intensity and the default density by using Lévy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution …