This book describes some models from the theory of investment which are mainly characterized by three features. Firstly, the decision-maker acts in a dynamic environment. Secondly, the distributions of the random variables are only incompletely known at the beginning of the planning process. This is termed as decision-making under conditions of uncer tainty. Thirdly, in large parts of the work we restrict the analysis to binary decision models. In a binary model, the decision-maker must choose one of two actions. For example, one decision means to undertake the invest ·ment project in a planning period, whereas the other decision prescribes to postpone the project for at least one more period. The analysis of dynamic decision models under conditions of uncertainty is not a very common approach in economics. In this framework the op timal decisions are only obtained by the extensive use of methods from operations research and from statistics. It is the intention to narrow some of the existing gaps in the fields of investment and portfolio analysis in this respect. This is done by combining techniques that have been devel oped in investment theory and portfolio selection, in stochastic dynamic programming, and in Bayesian statistics. The latter field indicates the use of Bayes' theorem for the revision of the probability distributions of the random variables over time.
Inhalt
1. Introduction.- 1.1 Uncertainty and Risk Aversion.- 1.2 Methods and Organization.- 2. The Monotonicity of Transition Probabilities.- 2.1 Sufficient Statistics.- 2.1.1 Sufficient Statistics for One-parameter Exponential Families.- 2.2 Posterior Distributions and Transition Probabilities.- 2.2.1 Definitions and Basic Properties.- 2.2.2 Monotone Transition Probabilities.- 2.2.3 Conjugate Prior Distributions.- 3. Dynamic Portfolio Models under Uncertainty.- 3.1 Classic Dynamic Portfolio Models.- 3.1.1 Risk Preferences.- 3.1.2 Classic Dynamic Portfolio Models under Risk.- 3.1.2.1 Assumptions.- 3.1.2.2 The Optimal Investment Policy and its Properties.- 3.1.2.3 Extended Versions of the Basic Model.- 3.1.3 Classic Dynamic Portfolio Models under Uncertainty.- 3.2 Binary Dynamic Portfolio Models under Uncertainty.- 3.2.1 The Return Distribution of the Risky Asset.- 3.2.2 The Stochastic Dynamic Program.- 3.2.2.1 Assumptions.- 3.2.2.2 Fundamental Properties.- 3.2.3 Properties of the Optimal Investment Policy.- 3.2.3.1 The Stopping Rule.- 3.2.3.2 The Monotonicity Property.- 3.2.3.3 The Stay-on-a-Winner-Property.- 3.2.4 Remarks on the Implementation of the Model.- 3.2.5 Sensitivity Analyses.- 3.2.5.1 An Algorithm for the Two-Point Return Distribution.- 3.2.5.2 Variation of the Utility Function.- 3.2.5.3 Variation of the Prior Distribution.- 3.2.5.4 Variation of the Planning Horizon.- 3.2.6 Conclusions.- 4. The Optimal Timing of Investment.- 4.1 Investment Decisions and the Economic Life of Projects.- 4.2 A Deterministic Model in Continuous Time.- 4.2.1 Net Cash Flows Independent of Project Age.- 4.2.2 Optimal Timing of Investment and Interest Rate.- 4.3 Investment Models under Conditions of Risk.- 4.3.1 Assumptions and the Optimal Investment Policy.- 4.3.2 A Survey of Already Known Models.- 4.3.3 Sensitivity Analyses and an Algorithm.- 4.4 Investment Models under Conditions of Uncertainty.- 4.4.1 The Influence of Uncertainty: An Example.- 4.4.2 The Explicit Formulation of Uncertainty.- 4.4.3 The Description as Binary Stopping Decision Model.- 4.4.4 Properties of the Optimal Investment Policy.- 4.4.5 The Comparison with Known Models.- 4.4.6 Sensitivity Analyses.- 4.4.6.1 Variation of the Capital Cost.- 4.4.6.2 Variation of the Riskless Interest Rate.- 4.4.6.3 Variation of the Planning Horizon.- 4.4.6.4 Variation of the Prior Distributions.- 4.4.6.5 The Certainty Equivalence Policy.- 4.4.7 The Optimal Exercise Date of an American Call Option.- 5. Concluding Remarks.- References.