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.
Study deep neural nets for solving complex insurance equations.
An unsupervised deep learning method solves PIDEs for option pricing.
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
Study of financial models using PIDEs with and without market liquidity.
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…
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…
This work integrates differentiation and integration in Physics-Informed Neural Networks.
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…
Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state of these systems which satisfy the Fokker-Planck equation or an integro-differen…
This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the impl…
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…
In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution in the scale of Bessel potential spaces. Our aim is to generalize known existenc…
The paper efficiently solves a complex option valuation equation for two assets.
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
Develops a PD estimation model using Lévy-driven processes for credit risk.
In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of som…
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We…
New deep learning method for option pricing in jump-diffusion models.
In this paper, we extend the jump-diffusion model proposed by Davis and Lleo to include jumps in asset prices as well as valuation factors. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constrai…
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution bri…
In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-diffe…
The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type and American-type geometri…
For , we present a generalized central limit theorem for -stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…
New model for Knightian uncertainty with jumps.
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to uni…
We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential…
One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneous…
The paper solves complex swing option pricing equations with numerical methods.
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted …
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 …
Investor optimizes portfolio under dynamic risk preferences.
Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochast…
New method uses PINNs to efficiently compute Gerber-Shiu functions.
Paper solves POMDPs in continuous time and discrete spaces.
Mean-field approximations simplify insurance liability calculations.
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…
We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump Lévy process. This model can capture both mean reversion and jumps which are observed in electricity market. It is shown that the value of an Eur…
We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forwa…
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…
Optimal dividend strategy with ratcheting and capital injection under Cramér-Lundberg model.
We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model numerically for two banks with jumps in their asset value processes. Specifically, we…
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…
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate the fair prices of such financial products, one needs appropriate models for the e…
Study forward investment performance in semimartingale markets with stochastic factors.
New method infers hidden states in continuous-time phenomena better than traditional models.
The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically pr…
Reinsurance counterparty credit risk (RCCR) is the risk of a loss arising from the fact that a reinsurance company is unable to fulfill her contractual obligations towards the ceding insurer. RCCR is an important risk category for insurance companies which, so far, has been addressed mostly via qualitative approaches. …