An asset in economic theory is a durable good which can only be partially consumed (like a portable music player) or input as a factor of production (like a cement mixer) which can only be partially used up in production.
As such, financial instruments like corporate bonds and common stocks are assets because they store value for the next period.
In a simple Walrasian equilibrium model, there is but a single period and all items have prices.
The subfield of asset pricing (or valuation) is the financial evaluation of the value of such assets; the primary method used by today's financial analysts is the discounted cash flow method.
With this method, an asset's future cash flows are either assumed to be known with certainty (as in a treasury bond which is risk free) or estimated.