Before we start this topic, it is important to say that playing music is not an olympic sport. You won't get a medal for playing louder than your colleagues in a concert. In fact, playing louder than everyone else is a rather rude and selfish thing to do. Remember: it's not about how loud you can play, it's about how loud you should play. With that in mind, open your ears and use your artistic taste to determine your dynamics. Don't let your physical ability to blow in your horn dictate how loud you will play.
Having said that, when the situation demands it, you need to be able to play a good forte or fortissimo. Developing a good dynamic range will take time and patience but if you work on it daily, you should see some fast progress.
Here are a few things you can do to make more sound:
1) long tones with 8 beats crescendo and 8 beats diminuendo. Doing a few of these daily will help your tone and increase your dynamic range.
2)Breathing exercises. Take deep breaths and stretch your harms at the same time making a "T" shape with your body. This will expand your rib cage and increase the air intake. Immediately pick up your instrument after a few breaths and play something. You'll be amazed how good it feels.
3) Fool around a bit. A few years ago, I asked a colleague who could play super loud how he did it. He said that he just spent a few weeks playing ridiculously loud just to fool around and that it worked for him...
4)Embouchure building techniques. If your chops are stronger, you will be more relaxed in the high register and will get a better air flow to make more sound.
5)Don't be shy! Play with confidence. Go for it and don't worry about missing some notes. Your audience wants to be entertained. They don't mind you missing as long as you really try. Fear of missing notes will make you hold back and you won't be able to play as loud as you want.
I'm sure there are a lot of other things you can do to turn up the volume but these 5 ideas should make a difference.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.