The definition of a dynamic character, is one who changes though the course of the story, as opposed to a static character, who does not change. Both the banker and the lawyer are dynamic characters.
The lawyer, young and boisterous at the beginning of the story, is greatly affected and changed by his fifteen year imprisonment. Though he endures much of it and seems to be changing positively (playing the piano, learning new languages, enrapturing himself in vigorous study), we see that at the end of his sentence he is emaciated and has aged greatly and for the worst. Though he easily won the bet (by remaining imprisoned for the entire 15 years) he leaves a day before his sentence is over, thereby forfeiting his winning. This shows the greatest change in character. He submits to being proven wrong and basically admits that he would have rather died than be shut up for 15 years in solitude.
The banker changes as a result of his circumstances. In the 15 years he keeps the lawyer prisoner, he loses all of his money and knows the reward he owes will destroy him. While he was a rich and seemingly honest man at the beginning of the story, his lack of wealth at the end drive him to dishonesty and even a plan for murder.
The changes of each character from the beginning of the story to the end could be considered extreme, which makes these men dynamic characters.