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Optimal Consumption And Investment With Bankruptcy
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Book Synopsis Optimal Consumption and Investment with Bankruptcy by : Suresh P. Sethi
Download or read book Optimal Consumption and Investment with Bankruptcy written by Suresh P. Sethi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Consumption and Investment with Bankruptcy by : Suresh Sethi
Download or read book Optimal Consumption and Investment with Bankruptcy written by Suresh Sethi and published by . This book was released on 2017 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Consumption and Investment Policies Allowing Consumption Constraints and Bankruptcy by : John P. Lehoczky
Download or read book Optimal Consumption and Investment Policies Allowing Consumption Constraints and Bankruptcy written by John P. Lehoczky and published by . This book was released on 2011 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Consumption-Investment Decisions Allowing for Bankruptcy by : Suresh Sethi
Download or read book Optimal Consumption-Investment Decisions Allowing for Bankruptcy written by Suresh Sethi and published by . This book was released on 2014 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Consumption and Investment Policies with Bankruptcy Modelled by a Diffusion with Delayed Reflection by : Suresh S. Sethi
Download or read book Optimal Consumption and Investment Policies with Bankruptcy Modelled by a Diffusion with Delayed Reflection written by Suresh S. Sethi and published by . This book was released on 1986 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients by : Abel Cadenillas
Download or read book Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients written by Abel Cadenillas and published by . This book was released on 2015 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy by : Monique Jeanblanc
Download or read book Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy written by Monique Jeanblanc and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Investment-consumption Models with Constraints by : Thaleia Zariphopoulou
Download or read book Optimal Investment-consumption Models with Constraints written by Thaleia Zariphopoulou and published by . This book was released on 1989 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Explicit Solution of a General Consumption/Investment Problem by : Ioannis Karatzas
Download or read book Explicit Solution of a General Consumption/Investment Problem written by Ioannis Karatzas and published by . This book was released on 2015 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Investment and Consumption with Transaction Costs by : Steven E. Shreve
Download or read book Optimal Investment and Consumption with Transaction Costs written by Steven E. Shreve and published by . This book was released on 1992 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Optimal Investment and Consumption When Allowing Terminal Debt by : An Chen
Download or read book Optimal Investment and Consumption When Allowing Terminal Debt written by An Chen and published by . This book was released on 2013 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze an optimal consumption and investment problem for a representative agent who may have different preferences for consumption and for terminal wealth. The utility for consumption is characterized by constant relative risk aversion so consumption is always positive. In contrast, the agent's risk aversion with regard to final wealth does not necessarily imply he must end up with positive terminal wealth. Indeed, we define the risk aversion for both positive and negative wealth levels and require it to be positive but not monotone. There is a point of maximal risk aversion at zero wealth and the agent may continue to consume when his wealth is negative.Using dual methods we can derive explicit solutions for this problem in a multi-asset economy which takes survival probabilities of the agent into account. This allows us to study the optimal patterns for consumption and investment and compare them to the case where terminal debt is not allowed.
Book Synopsis Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy by : Kexin Chen
Download or read book Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy written by Kexin Chen and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subsistence consumption and investment problems with bankruptcy are classic constrained stochastic optimal control problem in financial economic, where the consumption rate should be greater than a positive number and the investor faces a bankruptcy payment. We derive novel asymptotic solution to this problem under the fast mean-reverting stochastic volatility model. We rigorously prove that the zeroth-order approximation for the optimal pair of consumption and investment strategies leads to the first-order accuracy of the objective function. In addition, this zeroth-order suboptimal consumption-investment pair is asymptotically optimal in a class of admissible trading strategy pairs.
Book Synopsis Optimal Consumption and Investment with Insurer Default Risk by : Bong-Gyu Jang
Download or read book Optimal Consumption and Investment with Insurer Default Risk written by Bong-Gyu Jang and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve the optimal consumption and investment problem in an incomplete market, where borrowing constraints and insurer default risk are considered jointly. We derive in closed-form the optimal consumption and investment strategies. We find two main results with quantitative analysis. On the one hand, the proportion of wealth invested in stocks could increase (decrease) as insurer default risk increases when wealth is low (high). On the other hand, the voluntary annuity demand could increase (decrease) as risk aversion increases when insurer default risk is small (large).
Book Synopsis Optimal Consumption and Investment Decisions Under Time-Varying Risk Attitudes by : Felix Hentschel
Download or read book Optimal Consumption and Investment Decisions Under Time-Varying Risk Attitudes written by Felix Hentschel and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: When finding the optimal consumption and investment decision rules of an individual, accounting for a change in the risk aversion over the life cycle is an important aspect. Different methods are suggested in the literature. This paper combines the two approaches of including a habit level (see e.g. Constantinides, 1990) and a coefficient of time-varying risk aversion (see e.g. Steffensen, 2011). The optimal decision rules are derived in a complete market and examined in a numerical analysis.Our findings show that with a coefficient of time-varying risk aversion, the shape of the decision rules, rather than just their magnitude, depends on the initial wealth of the individual. Furthermore, a time-increasing risk aversion and sufficiently large habit formation lead to a hump-shaped consumption pattern and a decreasing investment into the risky asset, as observed in the literature.
Book Synopsis Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems by : Houmin Yan
Download or read book Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems written by Houmin Yan and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.
Book Synopsis Optimal Consumption and Investment Strategies with a Perishable and an Indivisible Durable Consumption Good by : Anders Damgaard
Download or read book Optimal Consumption and Investment Strategies with a Perishable and an Indivisible Durable Consumption Good written by Anders Damgaard and published by . This book was released on 2000 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the consumption and investment choice of an agent in a continuous-time economy with a riskless asset, several risky financial assets, and two consumption goods, namely a perishable and a durable good with an uncertain price evolution. Assuming lognormal prices and a multiplicatively separable, isoelastic utility function, we provide an explicit Merton-type solution for the optimal strategies for the case where the durable (and all other assets) can be traded without transaction costs. For the case where the durable good is indivisible, in the sense that durable trades imply transaction costs proportional to the value of the current durable holdings, we show analytically that the optimal durable trading strategy is characterized by three constants underline{z} lt; z* lt; overline{z}. As long as the ratio z of the total current wealth to the value of current durable holdings of the investor is in ( underline{z}, overline{z}), it is optimal not to trade the durable. At the boundaries of this interval it is optimal to trade the durable to attain z = z*. The model is used to examine the optimal substitution between perishable and durable consumption and the importance of the durable price uncertainty and the correlation between the price of the durable good and financial asset prices.
Book Synopsis Optimal Investment and Consumption Strategy for a Retiree Under Stochastic Force of Mortality by : Kanav Gupta
Download or read book Optimal Investment and Consumption Strategy for a Retiree Under Stochastic Force of Mortality written by Kanav Gupta and published by . This book was released on 2020 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: With an increase in the self-driven retirement plans during past few decades, more and more retirees are managing their retirement portfolio on their own. Therefore, they need to know the optimal amount of consumption they can afford each year, and the optimal proportion of wealth they should invest in the financial market. In this project, we study the optimization strategy proposed by Delong and Chen (2016). Their model determines the optimal consumption and investment strategy for a retiree facing (1) a minimum lifetime consumption, (2) a stochastic force of mortality following a geometric Brownian motion process, (3) an annuity income, and (4) non-exponential discounting of future income. We use a modified version of the Cox, Ingersoll, and Ross (1985) model to capture the stochastic mortality intensity of the retiree and, subsequently, determine a new optimal consumption and investment strategy using their framework. We use an expansion method to solve the classic Hamilton-Jacobi-Bellman equation by perturbing the non-exponential discounting parameter using partial differential equations.
