Gravitational Properties of Asteroids How large would an asteroid have to be in order to hold a person so that the person could not escape?
Of course you would need to specify who the person is - an Olympic athlete? Let us assume so and then you can scale downwards accordingly.

So an Olympic high jumper can jump hard enough to raise their centre of gravity about 2m off the ground. 

Let us assume this is a ballistic problem. The athlete actually gives themselves sufficient upward speed to get their centre of gravity from about 1m to 2m in the Earth's gravitational field. Using the usual equations for uniform acceleration, the required initial velocity is $v \simeq \sqrt{2gh} = 4.4$ m/s.

Now let us assume that the athlete could deliver something similar on an asteroid. This is doubtful, because getting a good run up, while wearing a spacesuit, is probably not going to happen. But if it were possible, then we just equate the jump velocity to the escape speed 
$$ v = \sqrt{\frac{2GM}{R}},$$
where $M$ and $R$ are the mass and the radius of the (assumed spherical) asteroid. 

Thus we do not have separate constraints on the mass and radius of the asteroid, only on their ratio. If
$$ \frac{M}{R} &gt; \frac{v^2}{2G},$$
then even an Olympic athlete couldn't jump into space.

To get something more definite we would need to assume a density, $\rho$, for the asteroid. This depends on what type of asteroid you are talking about, but could be between 1500 and 5000 kg/m$^3$ (Carry 2012).

If we assume (spherical asteroid again) that $M = 4\pi R^3 \rho/3$ and substituting this for the mass, we get a constraint on the asteroid radius such that someone is trapped if:
$$ R &gt; 4.2 \left(\frac{v}{4.4\ {\rm m/s}}\right) \left(\frac{\rho}{2000\ {\rm kg/m}^3}\right)^{-1/2}\ {\rm km}$$

You can mess about with this and assume a different take-off speed (you might want to argue, as MarkP does, that you could work up a larger horizontal speed by just running fast - but I doubt that in a "milligravity environment" - the surface gravity is of order 0.002 m/s$^2$) or different asteroid densities to modify the answer (trans-Neptunian objects or comets have densities lower than 1000 kg/m$^3$). Or you could come up with an equivalent constraint on the mass by substituting for $R$ in terms of the mass and density instead.