We develop a method to fi nd approximate solutions, and their accuracy, to consumption-investment problems with isoelastic preferences and in nite horizon, in incomplete markets where state variables follow a multivariate di ffusion. We construct upper and lower contractions, fi ctitious...

We propose a new optimal consumption model in which the degree of addictiveness of habit formation is directly controlled through a constraint on admissible consumption. In particular, we assume that the individual is unwilling to consume at a rate below a certain proportion 0α≤1 of her...

We formulate an infinite-horizon optimal investment and consumption problem, in which an individual forms a habit based on the exponentially weighted average of her past consumption rate, and in which she invests in a Black-Scholes market. The individual is constrained to consume at a rate...

We formulate and solve a deterministic optimal consumption problem to maximize the discounted CRRA utility of an individual’s consumption-to-habit process assuming she only invests in a riskless market and that she is unwilling to consume at a rate below a certain proportion α∈(0, 1] of her...

We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is...