abstract:
Many option pricing and portfolio selection problems in mathematical finance can be reformulated in terms of backward SDEs (BSDEs). As the corresponding BSDE can rarely be solved in closed form, simulation of BSDEs is of prime importance. However, the quality of the simulated solution depends on the interplay of different error sources, such as the discretization error, the simulation error, and e. g. the choice of basis functions (if the conditional expectations are estimated by least squares Monte Carlo). In this talk we suggest an error criterion which can be calculated explicitly in terms of the simulated solutions. Under suitable conditions it can be shown that this observable error criterion converges to zero at the same rate as the simulated solution converges to the unknown true solution. Finally, we illustrate how this error criterion can be applied to judge the quality of simulated solutions for some non-linear option pricing problems. |