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I am attempting to derive early exercise boundaries for American calls paying both continuous and fixed discrete dividends using the combination method from integral equations.

I have successfully reproduced the method described in work by Kallast and Kivin in python, but it only accounts for continuous div. Work by Meyer includes discrete divs, but only for put, as well as few others I have found so far.

Is it particularly difficult to derive boundary for American calls with these properties?

Also, I am attempting to approximate the discontinuity in the boundary for puts using tj∗ = tj − ln(1 + D/K)/r and interpolation with continuous div boundary before the ex-date on tj - is this a good way to approximate?

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Thank you.

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