Numerical Methods For Backward Stochastic Differential Equations With Jumps And Application In Finance

There are many phenomenon can use mathematical models to describe in nature, we can make a scientific explanation and prediction based on the research of the mathematical models, and then provide a reasonable way and effective method to solve these problems.Backward stochastic differential equations can be used for pricing financial derivatives, measure risk, assess risk and control financial problems in complex financial random environment. B-S option pricing formula play an important function in the derivatives market, it gives the option price in a risk-neutral market. The development of backward stochastic differential equations also promote the progress of financial market, more and more scholars devoted a lot of efforts to study its numerical solution, and got some perfect results.This paper studies a special model about BSDE, we got the discrete form by the approximation of integral, conditional expectation, Brownian motion, Poisson process, martingale and so on. We get a numerical solution of backward stochastic differential equations in theory.Innovation of this paper:we got a special class of backward stochastic differential equations with jumps under the numerical solution. By discrete the known backward stochastic differential equations with jump, we proved the discrete form of error, ultimately got the convergence order.