Your best bet is to prove to them that you've done the research necessary to protect your money, and that you're not like the millions of other investors that risk their money gambling in the market.

If you haven't already - spend some time researching stock market terminology, fundamental analysis, and basic financial accounting. Lay out a plan to consistently achieve winning trades, then present this to your parents. If you can show them you're serious about what you're doing, they should support your effort.

You will need to show them that you can make money out of it.

Try http://www.boilerroomtrader.com as its a virtual stock market simulator. Trade for free there with fake money. try making money there and then show them the stats.

I'm a high school student. I've made about $700 doing landscaping over the last year, and I want to start investing in the stock market. I have spent some time on stock market simulator, and now I want to try it for real. However, my parents aren't really risk-takers, so how can I ask them to set up an account for me, because I am a minor? Do you have any advice?