Optimal Investment Consumption And Retirement Choice Problem With Disutility And Subsistence Consumption Constraints
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| Author | : Byung Hwa Lim |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.
| Author | : Byung Hwa Lim |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
In this paper we consider a general consumption, portfolio and retirement optimization problem in which a working investor has borrowing constraints. Closed-form solutions are obtained for the utility maximization problems, and numerical procedures are given for the general utility function under borrowing constraints. Moreover we apply the results to the special utility function, the constant elative risk aversion (CRRA) utility function, and its numerical results suggest that the restriction to borrow future labor income makes the investor retire in a lower critical wealth level than in the case of no borrowing constraints.
| Author | : Suresh P. Sethi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461562570 |
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.
| Author | : Hyun Jin Jang |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : |
| ISBN | : |
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.
| Author | : Bahaaeddin Alareeni |
| Publisher | : Springer Nature |
| Total Pages | : 2139 |
| Release | : 2021-03-12 |
| Genre | : Technology & Engineering |
| ISBN | : 3030692213 |
This book introduces the students, researchers and practitioners into the subject and enabling technologies and applications pertaining to of technology, entrepreneurship and business development through research articles, case studies etc. It is primarily intended for academic purposes for learners of computer Science, management, accounting and information systems disciplines, economics,- entrepreneurship. Publishing chapters in the book is new innovative idea to spread the book in the Middle East and Arab countries and make the book achieve more sales. As many students in all levels, graduates and undergraduates in addition to research, professionals are not able to get sufficient resources because of the language concern.
| Author | : Junkee Jeon |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2020 |
| Genre | : |
| ISBN | : |
The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in his/her consumption throughout his/her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent's optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the von-Neumann-Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent's felicity utility function and depends only on the subjective discount rate and market parameters.
| Author | : Giorgio Ferrari |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2023 |
| Genre | : |
| ISBN | : |
This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: wealth, labor income, and force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional degenerate optimal stopping problem with interconnected dynamics. We establish the existence of an optimal retirement boundary that splits the state space into continuation and stopping regions. Regularity of the optimal stopping value function is derived and the boundary is proved to be Lipschitz continuous, and it is characterized as the unique solution to a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus retires whenever her wealth exceeds an age-, labor income- and mortality-dependent transformed version of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including the sensitivities of the optimal retirement boundary concerning the relevant model's parameters.
| Author | : Suresh Sethi |
| Publisher | : |
| Total Pages | : 444 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
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 co-authors (Abel Cadenillas, Myron Gordon, Brian Ingham, Ioannis Karatzas, John Lehoczky, Ernst Presman, Steven Shreve, and Michael Taksar) 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. Foreword by Harry M. Markowitz. Not included are Chapters 2, 3 and 13, which are available directly from the websites of the specified journals in which they first appeared.
| Author | : Inderjit Singh |
| Publisher | : |
| Total Pages | : 360 |
| Release | : 1986 |
| Genre | : Agricultural industries |
| ISBN | : |
This book presents the basic model of an agricultural household that underlies most of the case studies undertaken so far. The model assumes that households are price-takers and is therefore recursive. The decisions modeled include those affecting production and the demand for inputs and those affecting consumption and the supply of labor. Comparative results on selected elasticities are presented for a number of economies. The empirical significance of the approach is demonstrated in a comparison of models that treat production and consumption decisions separately and those in which the decisionmaking process is recursive. The book summarizes the implications of agricultural pricing policy for the welfare of farm households, marketed surplus, the demand for nonagricultural goods and services, the rural labor market, budget revenues, and foreign exchange earnings. In addition, it is shown that the basic model can be extended in order to explore the effects of government policy on crop composition, nutritional status, health, saving, and investment and to provide a more comprehensive analysis of the effects on budget revenues and foreign exchange earnings. Methodological topics, primarily the data requirements of the basic model and its extensions, along with aggregation, market interaction, uncertainty, and market imperfections are discussed. The most important methodological issues - the question of the recursive property of these models - is also discussed.
| Author | : Pedro Belli |
| Publisher | : World Bank Publications |
| Total Pages | : 294 |
| Release | : 2001-01-01 |
| Genre | : Business & Economics |
| ISBN | : 9780821348505 |
This books presents general principles and methodologies of quantitative risk analysis; provides theory and practice of how to evaluate health, transport and education projects and describes how to assess the environmental impact of projects. It looks at how the tools of cost benefit analysis can be applied from the point of view of the private sector, public sector, bankers, and the country as a whole. It encourages analysts to answer a number of key questions that are likely to increase success rather than simply describing techniques. This book as aimed at all concerned with resource allocation and is presented in an accessible fashion. It is required reading at World bank Institute courses.
