How to make MP4 and MPG-2 720 x 1280 videos? (aspect ratio 9:16)
You need to make sure your artwork is at least 720x1280 in size.  

Then open a video editing package like Adobe Premiere, Final Cut, or an animation package like After Effects.

Create a project with a canvas of 720 x 1280 pixels, and drag your artwork into it.

Make the timeline 10 seconds in duration (set in and out points on your timeline).

Export your timeline either in a higher quality video format first (like Apple ProRes 422 if you're in Final Cut), or export straight into the format your want (not all editing software exports in these formats).

If your software doesn't export in these formats, convert your ProRes file into the correct format using something like Adobe Media Encoder, Compressor, MPEG Streamclip, or Quicktime Pro 7.

Make sure you know what bit rate, frame rate, and color depth the video should be encoded at - ask whoever you're delivering to.  Set these when you do the export.

NB - I'm assuming 9x16 isn't a typo - most displays are 16x9 (16 horizontally and 9 vertically).  But as you said advertising displays, these are often in "portrait", i.e 9x16 aspect ratio.