french bow hold question

[Rob Menapace]

I've been studying classical bass method for about 2.5 years, as my work schedule allows. I use the same bow hold as my teacher, thumb on frog, middle finger reaches down enough to grasp the hair a little. Does this hold sound familiar to anyone? Or does anyone know of the origins of this hold? It seems common for french players to put their thumb on the stick. I know it's a matter of personal preference, but are there general strengths and weaknesses associated to these different bow holds?