Pricing barrier options with discrete dividends
  The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we compare the analytic approach, developed and effective for European puts and calls, of Buryak and Guo with the formulas, designed in the context of barrier option pricing, of Dai and Chiu. 
D. Jason Gibson, Aaron Wingo
q-fin.PR