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Feb 5, 2015 at 19:51 comment added bernhard This is a nice differential equation type solution. As a variation I would set $F(t) = e^{rT} e^{rS} e^{(1-r)(T+S)}$ and observe its zero derivative and compare $F(1)$ and $F(0)$ ...
Feb 5, 2015 at 12:21 comment added Denis Serre This is actually the method (in a simpler context though) to prove Campbell-Hausdorff's formula.
Feb 5, 2015 at 9:44 history answered gsa CC BY-SA 3.0