Okay, so there's a little bit of a problem. You want to find another, non wasteful, non landfill way of disposing of your fruit and veg waste. The little (easily solvable) problem is, you can't just put only that type of waste into a compost bin, because it will get very smelly, you will need to add some browns (carbon) because your fruit and veg waste counts as greens (nitrogen). Browns (carbon) could be something as simple as crumpled newspaper or torn up cardboard, but you will need to add some. There's a fairly relaxed explanation of browns and greens and C:N ratio here http://www.gardenmyths.com/how-to-compost-browns-greens/
Once you've read that (it's not very long) have a look at this video https://youtu.be/RE5hMhWBSRk - it may not be scientific in the way it uses what's readily available for browns, nor does it mention any kind of measurement, but it should work quite well. I think the receptacle shown in the video is a plastic dustbin with a clip on lid that has had holes drilled into it, rather than a custom made compost bin, but up to you what kind of bin you use. If you choose a tumbler type compost bin, one that you can rotate, make sure you have enough room on your balcony to actually rotate it periodically, although to be honest, it will still compost down over time with or without rotation. If you do not rotate it, and leave it alone to do its thing, just adding to it periodically, it will not be suitable for use in pots, but it doesn't sound like that's what you wanted to do with it anyway.
UPDATE: I can't see any reason why it can't be put in the forest, unless you know someone with a garden who might value it - it's nutritious stuff you know, brilliant for soil and plants.