In this paper, we propose a general methodology to characterize (i.e. develop the recursive equation systems for) the dynamic stochastic general equilibrium asset pricing problems (DSGE) with arbitrary numbers of agents and financial assets in a Lucas economy and propose a convergent numerical...

In this paper, we introduce a clustering method to approximate the solution to a general Backward Stochastic Differential Equation with Jumps (BSDEJ). We show the convergence of the sequence of approximate solutions to the true one. The method is implemented for an application in finance....

In this paper, we combine the theory of stochastic process and techniques of machine learning with the regression analysis, first proposed by Longstaff and Schwartz 2001 and apply the new methodologies on financial derivatives pricing. Rigorous convergence proofs are provided for some of the...