In insurance mathematics, optimal control problems over an infinite time horizon arise when
computing risk measures. An example of such a risk measure is the expected discounted …

This paper proposes a non-parametric technique of option valuation and hedging. Here, we
replicate the extended Black–Scholes pricing model for the exotic barrier options and their …

This paper compares two statistical methods for parameter reconstruction (random drift and
diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of …

We propose an accurate data-driven numerical scheme to solve stochastic differential
equations (SDEs), by taking large time steps. The SDE discretization is built up by means of …

In this paper, we study the problem of solving Seal's type partial integro-differential
equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep …

Efficient algorithms for solving high-dimensional partial differential equations (PDEs) has
been an exceedingly difficult task for a long time, due to the curse of dimensionality. We …

Reflected partial differential equations (PDEs) have important applications in financial
mathematics, stochastic control, physics, and engineering. This paper aims to present a …