Optimal Investment Consumption And Retirement Decision With Disutility And Borrowing Constraints
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| 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 | : 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 | : Seyoung Park |
| Publisher | : |
| Total Pages | : |
| Release | : 2016 |
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I study optimal consumption and investment for retirement in an economic environment where an individual has retirement flexibility and borrowing constraints. I show that Friedman's (1957) permanent income hypothesis (PIH) is generalized with retirement and constrained borrowing against future labor income. In particular, a linear consumption rule in financial wealth and human wealth does not hold, and the non-linearity feature of option associated with retirement is of great importance to the consumption policy. Further, the first-order effect of inability to borrow money with human wealth on consumption and savings for retirement is captured by the generalized PIH rule. Finally, I find that an individual's aggressive risk taking by increasing stock investment turns out to be somewhat rational for retirement.
| Author | : L. C. G. Rogers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 163 |
| Release | : 2013-01-10 |
| Genre | : Mathematics |
| ISBN | : 3642352022 |
Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.
| Author | : |
| Publisher | : |
| Total Pages | : 75 |
| Release | : 2016 |
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| 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 | : James Benjamin Taylor (Jr.) |
| Publisher | : |
| Total Pages | : 85 |
| Release | : 2013 |
| Genre | : Electronic dissertations |
| ISBN | : |
We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem with a sequence of discrete-time Markov chain control problems by applying dynamic programming and the Markov chain approximation. We demonstrate how the problem can be solved numerically through a logarithmic transformation of the investor's wealth variable, even when the utilities are CRRA with large risk aversion parameter. The model and computational approach are applied to a retiree's optimal annuity decision in the presence of default risk, and we demonstrate that default risk can lead a retiree to annuitize significantly smaller proportions of savings, even when a portion of the defaulted annuity can be recovered, than is traditionally considered optimal by the retirement-finance community. Hence, we show that credit risk may play an important role in resolving the annuity puzzle.
| Author | : Matthew M. Woolley |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2004 |
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| ISBN | : |
This paper characterizes optimal consumption and investment policies for investors with asset return predictability, stochastic labor income and endogenously-determined retirement. We find that the ratio of total wealth-to-labor income (normalized wealth) is the primary determinant of the retirement decision and that at all ages, there exists a critical normalized wealth such that above this wealth, investors retire. We further consider the implications of endogenous retirement on portfolio choice. It is well known that human capital plays a large role in the determination of optimal equity proportion in financial portfolios. By endogenizing retirement, human capital becomes dependent on savings and investment decisions, which in turn depend on human capital. When compared to investors who exogenously retire at age 65, we find that low-wealth investors with the option to time retirement invest more aggressively while investors with slightly greater normalized wealth invest less aggressively prior to retirement. Investors with high normalized wealth behave almost the same as in the exogenous retirement case. This result contrasts the results in two recent papers and is due to the existence of stochastic labor income. Finally, we consider the impact of asset return/labor income correlation and find that equity holdings are nearly completely crowded-out by increased labor income (background) risk.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 749 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 0444633898 |
Handbook of Behavioral Economics: Foundations and Applications presents the concepts and tools of behavioral economics. Its authors are all economists who share a belief that the objective of behavioral economics is to enrich, rather than to destroy or replace, standard economics. They provide authoritative perspectives on the value to economic inquiry of insights gained from psychology. Specific chapters in this first volume cover reference-dependent preferences, asset markets, household finance, corporate finance, public economics, industrial organization, and structural behavioural economics. This Handbook provides authoritative summaries by experts in respective subfields regarding where behavioral economics has been; what it has so far accomplished; and its promise for the future. This taking-stock is just what Behavioral Economics needs at this stage of its so-far successful career. - Helps academic and non-academic economists understand recent, rapid changes in theoretical and empirical advances within behavioral economics - Designed for economists already convinced of the benefits of behavioral economics and mainstream economists who feel threatened by new developments in behavioral economics - Written for those who wish to become quickly acquainted with behavioral economics
| Author | : Theo S. Eicher |
| Publisher | : MIT Press |
| Total Pages | : 343 |
| Release | : 2007-01-26 |
| Genre | : Business & Economics |
| ISBN | : 0262550644 |
Even minute increases in a country's growth rate can result in dramatic changes in living standards over just one generation. The benefits of growth, however, may not be shared equally. Some may gain less than others, and a fraction of the population may actually be disadvantaged. Recent economic research has found both positive and negative relationships between growth and inequality across nations. The questions raised by these results include: What is the impact on inequality of policies designed to foster growth? Does inequality by itself facilitate or detract from economic growth, and does it amplify or diminish policy effectiveness? This book provides a forum for economists to examine the theoretical, empirical, and policy issues involved in the relationship between growth and inequality. The aim is to develop a framework for determining the role of public policy in enhancing both growth and equality. The diverse range of topics, examined in both developed and developing countries, includes natural resources, taxation, fertility, redistribution, technological change, transition, labor markets, and education. A theme common to all the essays is the importance of education in reducing inequality and increasing growth.
