No you cannot run your own advertising and there is no upgrade aside from a VIP hosting upgrade that you can purchase that allows it on a free hosted WordPress.com blog.
There is only one advertising program called WordAds at WordPress.com and it’s for blogs on their own domains. Aside from a blog being accepted into WordAds http://www.wordads.co/ no blogger initiated advertising, retailing or reselling the work or products created or services provided by anyone other than yourself is allowed on free hosted wordpress.com blogs.
E-commerce transactions via shopping carts and the like cannot be conducted on free blogs from and being free hosted by WordPress.com. Paid content and/or sponsored content is not allowed.
http://en.support.wordpress.com/advertising/
http://en.wordpress.com/types-of-blogs/
http://en.support.wordpress.com/affiliate-links/
http://en.support.wordpress.com/suspended-blogs/
http://en.wordpress.com/tos/
On free hosted WordPress.com blog we can use a contact form and/or a PayPal donation button for sale of only products or services created or provided by ourselves.
http://en.support.wordpress.com/paypal/
http://en.support.wordpress.com/contact-form/
If you do require an ecommerce site, advertising, affiliate links, paid or sponsored content you can hire a web host and get a free software install from http://wordpress.org
Refer to > http://support.wordpress.com/com-vs-org/
http://en.support.wordpress.com/moving-a-blog/