This thesis elaborates on the wealth maximization problem of a small investor who invests in a financial market. Key tools for our studies come across in the form of several classes of BSDEs with particular non-linearities, casting them outside the standard class of Lipschitz continuous BSDEs....

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices...

Varian (1988) showed that the utility maximization hypothesis cannot be falsified when only a subset of goods is observed. We show that this result does not hold under the assumptions that unobserved prices and expenditures remain constant. These assumptions are naturally satisfied in laboratory...