We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the form a
0 / N
1/2 + a
1 / N
3/2 + · · · + b
1 / N + b
2 / N
2 + b
4 / N
4
+ · · ·, where N is the number of monitoring intervals. We obtain explicit expressions for the coefficients {a
0, a
1, …, b
1, b
2, …}. In particular, a
0 is proportional to the value of the Riemann zeta function at ½, a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.