Before revision:  The pricing kernel is given by the product of a discount factor and the Esscher martingale associated with the risk aversion parameter. The model is fixed by the requirement that for each asset the product of the asset price and the pricing kernel should be a martingale. In the GBMcase , the risk aversion factor is the so-called market price of risk.
After revision:  The pricing kernel is given by the product of a discount factor and a risk aversion martingale. For GBM , the risk aversion factor is the so-called market price of risk.