In finace, a barrier option is a type of financial optioin where the option to exercise depends on the underlying crossing or reaching a given barrier level. Barrier options were created to provide the insurance value of an option without charging as much premium. For example, if you believe that IBM will go up this year, but are willing to bet that it won't go above $100, then you can buy the barrier and pay less premium than the vanilla option.

lz知道怎么推导障碍期权的理论价格公式么？可以参阅Bjork的 'Arbitrage Theory in Continuous Time' 2ed.

至于pde的验证么，你可以参考pde数值解法的有限差方法(finite difference),可以参考Tools for Computational Finance 3rd edition,published by Springer.

可以参考R. Zvan的PDE methods for pricing barrier options

Journal of Economic Dynamics & Control
24 (2000) 1563}1590