We propose a new forward-backward stochastic differential equation solver for highdimensional derivative pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our...

We provide solution formulas for (linear and non-linear) jump-diffusion backward stochastic differential equations (BSDEs) under diverse enlarged filtration approaches. We also derive a comparison theorem for BSDEs in an enlarged filtration framework and present several applications of our...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

Adomain decomposition method is a powerful technique to solve nonlinear differential equations and nonlinear Integro - differential equations. This paper presents a novel way of computing Adomian polynomials for nonlinear terms occur in nonlinear differential equations through partial Bell...

The trajectories of particles moving in a real line and following the Geometrical Brownian motion have been studied. We take processes and give the generalization of the notions, descriptions and models of Geometrical Brownian motion with bouncing. Moreover, we derive the formulas, which enable...

Stochastic Calculus deals with the rate of change of functions with respect to the randomness. It has been applied in the field of financial mathematics. When we look at the graph of stock prices, there are many irregular price fluctuations. The main tool for modeling the small fluctuations is...

We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is...

We characterize the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is...

In this paper, enlightened by the asymptotic expansion methodology developed by Li (2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by the gamma processes, a special type of Levy processes....

We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional...