Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep neural network algorithms for solving linear and semilinear parabolic partial integro-differential equations with boundary conditions in high dimension. To show the viability of our approach we discuss several case studies from insurance and finance.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high…
Linear and Nonlinear Partial Integro-Differential Equations arising from Finance
The purpose of this review paper is to present our recent results on nonlinear and nonlocal mathematical models arising from modern financial mathematics. It is based on our four papers written jointly by J. Cruz, M. Gro…
Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps
We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the j…
Deep LearningMean-variance hedging of unit linked life insurance contracts in a jump-diffusion model
We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium.…
INEUS: Iterative Neural Solver for High-Dimensional PIDEs
In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling a…