We revisit the influential economic growth model by Lucas (1988) ["On the mechanics of economic development." Journal of Monetary Economics, 22(1):3-42], assuming that households optimally allocate consumption and education over the life-cycle given an exogenous interest rate and exogenous...

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.