This is an exercise from a probability textbook on Ito's formula, basically Ito's formula extends to functions of this type.
Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f$ is twice differentiable everywhere except on a set $\{a_1,...a_k\}$. At these isolated points, $f'(a_n+)$ $f'(a_n-)$ $f''(a_n+)$ and $f''(a_n-)$ exists. (These are the left and right limits of $f'$ and $f''$ at these points.)
The question is: how can we show such a function is the difference of two convex functions.
I would also be interested in the following question:
Which conditions could we have weakened such that it is still the difference of two convex functions?