Synopses & Reviews
The problem of optimal consumption and investment is concerned with the decisions of a single agent endowed with some initial wealth who seeks to maximize total expected discounted utility of consumption. The decisions are the rate of consumption and the allocation of their wealth directed to risky and risk-free investments over time. The problem was first studied by Paul Samuelson and Robert Merton in 1969; however none of their formulations took into account the possibility that an agent might go bankrupt in the process. In a set of articles published in 1979 and 1983, Suresh Sethi and various co-authors explicitly introduced a bankruptcy value/penalty in the consumption/investment model. In addition, they also introduced a nonzero subsistence consumption level, which makes the consideration of bankruptcy even more important. This provided the ability to deal mathematically with the problems of bankruptcy in the study of consumption and investment. Optimal Consumption and Investment with Bankruptcy provides a useful frame for deepening our understanding of the consumption and portfolio selection behavior of individuals and households.
Synopsis
This book presents papers on continuous-time consumption- investment models by Suresh Sethi and various co-authors. Sir Isaac Newton said that he saw so far because he stood on the shoulders of gi- ants. Giants upon whose shoulders Professor Sethi and colleagues stand are Robert Merton, particularly Merton's (1969, 1971, 1973) seminal papers, and Paul Samuelson, particularly Samuelson (1969). Karatzas, Lehoczky, Sethi and Shreve (1986), henceforth KLSS, re- produced here as Chapter 2, reexamine the model proposed by Mer- ton. KLSS use methods of modern mathematical analysis, taking care to prove the existence of integrals, check the existence and (where appro- priate) the uniqueness of solutions to equations, etc. KLSS find that un- der some conditions Merton's solution is correct; under others, it is not. In particular, Merton's solution for aHARA utility-of-consumption is correct for some parameter values and not for others. The problem with Merton's solution is that it sometimes violates the constraints against negative wealth and negative consumption stated in Merton (1969) and presumably applicable in Merton (1971 and 1973). This not only affects the solution at the zero-wealth, zero-consumption boundaries, but else- where as well. Problems with Merton's solution are analyzed in Sethi and Taksar (1992), reproduced here as Chapter 3.
Table of Contents
Foreword; Harry M. Markowitz. Preface. Part I: Introduction. 1. Consumption/Investment Problems. Part II: Models with Constant Market Parameters and Nonnegative Consumption. 2. Explicit Solution of a General Consumption/Investment Problem. 3. A Note on Merton's `Optimum Consumption and Portfolio Rules in a Continuous-Time Model'. 4. Infinite-Horizon Investment Consumption Model with a Nonterminal Bankruptcy. 5. Risk-Aversion Behavior in Consumption/Investment Problems. Part III: Models with Constant Market Parameters and Positive Subsistence Consumption. 6. Explicit Solution of a General Consumption/Portfolio Problem with Subsistence Consumption and Bankruptcy. 7. Distribution of Bankruptcy Time in a Consumption/Portfolio Problem. 8. Risk-Aversion Behavior in Consumption/Investment Problems with Subsistence Consumption. 9. Consumption Behavior in Investment/Consumption Problems. 10. Equivalence of Objective Functionals in Infinite Horizon and Random Horizon Problems. 11. A Contribution to the Micro Foundation for Keynesian Macroeconomic Models. Part IV: Models with More General Markets and Positive Subsistence Consumption. 12. The Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients. Part V: Models with Constant Market Parameters, Positive Subsistence Consumption and Borrowing/Shortselling Constraints. 13. Optimal Dynamic Consumption and Portfolio Planning in a Welfare State. 14. Optimal Consumption and Investment Policies Allowing Consumption Constraints, Bankruptcy and Welfare. 15. A Martingale Formulation for Optimal Consumption/Investment Decision Making. Part VI: Conclusions. 16. Concluding Remarks and Open Research Problems. Author Index. Copyright Permissions.