A Case Study in Analog Co-Processing for Solving Stochastic Differential Equations

Stochastic differential equations (SDEs) are an important class of mathematical models for areas such as physics and finance. Usually the model outputs are in the form of statistics of the dependent variables, generated from many solutions of the SDE using different samples of the random variables. Challenges in using existing conventional digital computer architectures for solving SDEs include: rapidly generating the random input variables for the SDE solutions, and having to use numerical integration to solve the differential equations. Recent work by our group has explored using hybrid analog-digital computing to solve differential equations. In the hybrid computing model, we solve differential equations by encoding variables as continuous values, which evolve in continuous time. In this paper we review the prior work, and study using the architecture, in conjunction with analog noise, to solve a canonical SDE, the Black-Scholes SDE.