We analyze the quantum dynamics of an exciton boser or laser - a devic
e that generates a coherent population of nonequilibrium excitons. Aft
er deriving the master equation for the exciton boser in the Born-Mark
ov approximation, we use a stochastic wave function approach to demons
trate that an approximately coherent state of excitons is generated fr
om the vacuum state. The quantum theory that we develop allows us to a
nalyze the effects of exciton-exciton interactions on coherent state f
ormation. We demonstrate that the line width reduction obtained in a b
oser is limited by the strength of these interactions.