This thesis consists, in excess to an introductory chapter, of five papers within the area of consumption and investment decision making. The unifying topic is optimization of a stochastic wealth process. The underlying investment market is for all five papers the celebrated Black-Scholes market. What differentiates the papers are different wealth dynamics, optimization objectives, and possibly restrictions on the wealth process. The first paper considers an investor, endowed with deterministic labor income, who searches to maximize expected cumulated utility from consumption and terminal wealth, while being restricted to keep wealth above a given barrier. The problem is solved by use of the Martingale Method for stochastic optimization problems in complete markets. The solution becomes an OBPI (option based portfolio insurance) strategy where the option bought to protect against losses in the unrestricted portfolio is an American put option. The second paper extends the ideas of the first paper in two ways. First, we consider an investor with an uncertain lifetime, thereby also including utility from bequest, and introduce the possibility to invest in a life-insurance market. Second, the wealth restriction is allowed to depend, in a general way, on the wealth process. This allows for an analysis of the widespread pension saving product where a minimum rate of return on pension contributions is guaranteed. The first two papers are summarized in Section 1.2, and the full papers are presented in Chapter 2 and 3, respectively. The third paper, summarized in Section 1.3 and presented in Chapter 4, contributes to the new area of consistent optimization within classes of inconsistent problems. More formally, a class of non-linear objectives, for which the Bellman Optimality Principle does not hold, is considered. The two key examples treated are the mean-variance and mean-standard deviation problems,including both consumption, labor income, and terminal wealth, for an investor without precommitment. As explained in the paper the term “without pre-commitment” refers to the fact that we look for optimal strategies in the sense of Nash equilibrium strategies. The forth paper of this thesis takes a utility approach to quantify the impact of investment costs. Concretely, we consider a power utility investor searching to maximize expected utilityfrom terminal wealth. The impact of investment costs is split into a direct loss and an indirect loss. The direct loss is due to paying investment costs, and the indirect loss is due to lost investment opportunities, caused by the investors risk aversion. The indirect loss is measured by an indifference compensation ratio, defined as the minimum relative increase in the initial wealth the investor demands in compensation to accept incurring investment costs of a certain size. The magnitude of the indirect loss turns out to be between the same as and half of the expected direct loss, i.e. surprisingly big. Finally, a related analysis allows us to conclude that the size of the investment costs is of far more importance than the specific choose of investment strategy. The paper is summarized in Section 1.4, and the full paper is presented in Chapter 5. Finally, the last paper, summarized in Section 1.5 and presented in Chapter 6, considers entrance times of random walks, i.e. the time of first entry to the negative axis. Partition sum formulas are given for entrance time probabilities, the nth derivative of the generating function,and the nth falling factorial entrance time moment. Similar formulas for the characteristic function of the position of the random walk both conditioned on entry and conditioned on no entry are also established. All quantities are also considered for the stationary process. The theoretical results are applied to analyze the widespread with-profit pension product. More precisely, exact (computable) formulas for the bonus time probabilities, the expected bonus size, and the expected funding ratio given no bonus are presented. Moreover, to conduct a meanvariance analysis for a fund in stationarity we devise a simple and effective exact simulation algorithm for sampling from the stationary distribution of a regenerative Markov chain.