You are only telling us one parameter pair when you mention driving 10MHz into 1kOhm. On the other side, you specifically ask for an ARBITRARY generator, whose purpose is generally to drive anything but sine! So I suspect that you have some other requirements as well. A output amplifier or booster for a arbitrary waveform generator should be specified for DC as well as for step functions, otherwise it's a output modifier (filter)!
Even if it was a erroneous designation and you do not need and ArbGen, it would be helpful to know more.
As mentioned above, there is the HP 3325A with option 002, which gives you 40Vpp, but triangle is limited to 11kHz (Sin to 21MHz, Square to 10MHz).
Also the nice little HP3314, which goes to 19.99MHz with option 001 would give you 30Vpp. (not sure about limitations, but this one does ARB)
I looked at my Analogic's and they do only 10Vpp into 50Ohms, same for the Prema ARB1000 and the SRS DS345. And those are fairly high-end. So you would need to go either for one of the devices with special options or use a booster. If you really need only the 10MHz SINE with 30Vpp into 1k, then somithing might be cobbled together using a modern power OPA and/or buffer IC.