Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the...

In an arbitrage free incomplete market we consider the problem of maximizing terminal isoelastic utility. The relationship between the optimal portfolio, the optimal martingale measure in the dual problem and the optimal value function of the problem is described by an BSDE. For a totally...

In both complete and incomplete markets we consider the problem of fulfilling a financial obligation xc as well as possible at time T if the initial capital is not sufficient to hedge xc. This introduces a new risk into the market and our main aim is to minimize this shortfall risk by making use...