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| Author | : Suresh P. Sethi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461562570 |
Download Optimal Consumption and Investment with Bankruptcy Book in PDF, ePub and Kindle
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 | : Suresh Sethi |
| Publisher | : |
| Total Pages | : 444 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
Download Optimal Consumption and Investment with Bankruptcy Book in PDF, ePub and Kindle
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 | : John P. Lehoczky |
| Publisher | : |
| Total Pages | : 114 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
Download Optimal Consumption and Investment Policies Allowing Consumption Constraints and Bankruptcy Book in PDF, ePub and Kindle
An agent can distribute his wealth between two investments, one with a fixed rate of return r and the other with a random rate of return (modeled as a diffusion) with mean r. The agent seeks to maximize total discounted utility from consumption over an infinite horizon. Consumption may be constrained from below. Various models for bankruptcy, including welfare, are considered. The agent has a strictly concave utility function for consumption; however, it is shown that the utility function for wealth may have convex portions, thus the agent may be risk seeking. The paper gives a complete treatment of the existence and nonexistence of optimal policies. New theorems for the optimal control of degenerate diffusions are given, as well as explicit formulas for the value function.
| Author | : Suresh Sethi |
| Publisher | : |
| Total Pages | : 39 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
Download Optimal Consumption-Investment Decisions Allowing for Bankruptcy Book in PDF, ePub and Kindle
This paper surveys the research on optimal consumption and investment problem of an agent who is subject to bankruptcy that has a specified utility (reward or penalty). The bankruptcy utility, modeled by a parameter, may be the result of welfare subsidies, the agent's innnate ability to recover from bankruptcy, psychic costs associated with bankruptcy, etc. Modeled with non-negative consumption, positive subsistence consumption, risky assets modeled by geometric Brwonian motions or semimartingales are discussed. The paper concludes with suggestions for open research problems.
| Author | : Suresh S. Sethi |
| Publisher | : |
| Total Pages | : 10 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
Download Optimal Consumption and Investment Policies with Bankruptcy Modelled by a Diffusion with Delayed Reflection Book in PDF, ePub and Kindle
A diffusion process with delayed reflection at zero is used to model wealth dynamic in a consumption/investment model. The speed of exit from the boundary corresponds to recovery rate from bankruptcy. An optimal behavior in the model is analyzed. Qualitative structure of the optimal feedback controls is described.
| Author | : Abel Cadenillas |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Download Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients Book in PDF, ePub and Kindle
We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal consumption and wealth processes in terms of the optimal bankruptcy time. This paper extends the results of Karatzas, Lehoczky, and Shreve on the maximization of expected utility from consumption in a financial market with random coefficients by incorporating subsistence consumption and bankruptcy. It also addresses the random coefficients and finite-horizon version of the problem treated by Sethi, Taksar, and Presman. The mathematical tools used in our analysis are optimal stopping, stochastic control, martingale theory, and Girsanov change of measure.
| Author | : Monique Jeanblanc |
| Publisher | : |
| Total Pages | : |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
Download Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy Book in PDF, ePub and Kindle
In this paper we consider the optimization problem of an agent who wants to maximize the total expected discounted utility from consumption over an infinite horizon. The agent is under obligation to pay a debt at a fixed rate until he/she declares bankruptcy. At that point, after paying a fixed cost, the agent will be able to keep a certain fraction of the present wealth, and the debt will be forgiven. The selection of the bankruptcy time is taken to be at the discretion of the agent. The novelty of this paper is that at the time of bankruptcy the wealth process has a discontinuity, and that the agent continues to invest and consume after bankruptcy. We show that the solution of a free boundary problem satisfying some additional conditions is the value function of the above optimization problem. Particular examples such as the logarithmic and the power utility functions will be provided, and in these cases explicit forms will be given for the optimal bankruptcy time, investment and consumption processes.
| Author | : Thaleia Zariphopoulou |
| Publisher | : |
| Total Pages | : 136 |
| Release | : 1989 |
| Genre | : Investments |
| ISBN | : |
Download Optimal Investment-consumption Models with Constraints Book in PDF, ePub and Kindle
| Author | : Ioannis Karatzas |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Download Explicit Solution of a General Consumption/Investment Problem Book in PDF, ePub and Kindle
This paper solves a general consumption and investment decision problem in closed form. An investor seeks to maximize total expected discounted utility of consumption. There are N distinct risky investments, modeled by dependent geometric Brownian motion processes, and one risk-less (deterministic) investment. The analysis allows for a general utility function and general rates of return. The model and analysis take into consideration the inherent non-negativity of consumption and consider bankruptcy, so this paper generalizes many of the results of Lehoczky, Sethi, and Shreve. The value function is determined explicitly, as are the optimal consumption and investment policies. The analysis is extended to consider more general risky investments. Under certain conditions, the value functions derived for geometric Brownian motion are shown to provide upper and lower bounds on the value functions in the more general context.
| Author | : Steven E. Shreve |
| Publisher | : |
| Total Pages | : 77 |
| Release | : 1992 |
| Genre | : Consumption (Economics) |
| ISBN | : |
Download Optimal Investment and Consumption with Transaction Costs Book in PDF, ePub and Kindle
Abstract: "A complete solution is provided to the infinite-horizon, discounted problem of optimal consumption and investment in a market with one stock, one money market (sometimes called a 'bond'), and proportional transaction costs. The utility function may be of the form c[superscript p]/p where p
