According to American economist F.B. Hawley, there is proportional relationship between risk and profit. Higher the risk of the entrepreneur, greater will his profit. On the contrary, lower the risk, lesser the profit.
When it comes to innovation, Prof. Schumpter who created the Innovation Theory of Profit, said that the function of the entrepreneur is to produce innovations for new inventions. Reward that an entrepreneur gets for innovating is called profit.
Prof. Schumpter claims that innovations are of 5 kinds: (1) The introduction of a new product; (2) The introduction of a new method of production; (3) The opening up of a new market; (4) The discovery of a new source of raw materials; and (5) The reorganization of an industry.
According to this theory, profit due to innovation is temporary. Other entrepreneurs imitate the innovation. Competition among the entrepreneurs grows and thus economic profits disappear.
The lure of profit encourages entrepreneurs to go in for more innovations. Thus innovations give rise to profits and lure of profit stimulates entrepreneurs to innovate.
Learn more about how these factors (risk, profit, innovation) are related from FK Publications' Economics (for BTM - 1).