Optimal Investment and Consumption Portfolio Choice Problem for Assets Modeled by Levy Processes PDF Download
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Author: Ryan G. Sankarpersad
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
ABSTRACT: We consider an extension of Merton's optimal portfolio choice and consumption problem for a portfolio in which the underlying risky asset is an exponential Levy process. The investor is able to move money between a risk free asset and a risky asset and consume from the risk free asset. Given the dynamics of the total wealth of the portfolio we consider the problem of finding portfolio weights and a consumption process which optimizes the investors expected utility of consumption over the investment period. The problem is solved in both the finite and infinite horizon cases for a family of hyperbolic absolute risk aversion utility functions using the techniques of stochastic control theory. The general closed form solutions are found for for the case of a power utility function and then for a more generalized utility. We consider a variety of Levy processes and make a comparison of the optimal portfolio weights. We find that our results are consistent with expectations that the greater the inherent uncertainty of a given process leads to a smaller fraction of wealth invested in the risky asset. In particular an investor is more careful when the risky asset is a discontinuous Levy process when compared to the continuous case such as those found in a geometric Brownian motion model.
Author: Ryan G. Sankarpersad
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
ABSTRACT: We consider an extension of Merton's optimal portfolio choice and consumption problem for a portfolio in which the underlying risky asset is an exponential Levy process. The investor is able to move money between a risk free asset and a risky asset and consume from the risk free asset. Given the dynamics of the total wealth of the portfolio we consider the problem of finding portfolio weights and a consumption process which optimizes the investors expected utility of consumption over the investment period. The problem is solved in both the finite and infinite horizon cases for a family of hyperbolic absolute risk aversion utility functions using the techniques of stochastic control theory. The general closed form solutions are found for for the case of a power utility function and then for a more generalized utility. We consider a variety of Levy processes and make a comparison of the optimal portfolio weights. We find that our results are consistent with expectations that the greater the inherent uncertainty of a given process leads to a smaller fraction of wealth invested in the risky asset. In particular an investor is more careful when the risky asset is a discontinuous Levy process when compared to the continuous case such as those found in a geometric Brownian motion model.
Author: Nicolas Chapados
Publisher: Springer Science & Business Media
ISBN: 1461405777
Category : Computers
Languages : en
Pages : 107
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Book Description
This brief offers a broad, yet concise, coverage of portfolio choice, containing both application-oriented and academic results, along with abundant pointers to the literature for further study. It cuts through many strands of the subject, presenting not only the classical results from financial economics but also approaches originating from information theory, machine learning and operations research. This compact treatment of the topic will be valuable to students entering the field, as well as practitioners looking for a broad coverage of the topic.
Author: John Y. Campbell
Publisher:
ISBN:
Category : Consumption (Economics)
Languages : en
Pages : 88
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Book Description
This paper proposes and implements a new approach to a classic unsolved problem in financial economics: the optimal consumption and portfolio choice problem of a long-lived investor facing time-varying investment opportunities. The investor is assumed to be infinitely-lived, to have recursive Epstein-Zin-Weil utility, and to choose in discrete time between a riskless asset with a constant return, and a risky asset with constant return variance whose expected log return follows and AR(1) process. The paper approximates the choice problem by log-linearizing the budget constraint and Euler equations, and derives an analytical solution to the approximate problem. When the model is calibrated to US stock market data it implies that intertemporal hedging motives greatly increase, and may even double, the average demand for stocks by investors whose risk-aversion coefficients exceed one.
Author: Sanford J. Grossman
Publisher:
ISBN:
Category : Assets (Accounting)
Languages : en
Pages : 76
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Book Description
We analyze a model of optimal consumption and portfolio selection in which consumption services are generated by holding a durable good. The durable good is illiquid in that a transaction cost must be paid when the good is sold. It is shown that optimal consumption is not a smooth function of wealth; it is optimal for the consumer to wait until a large change in wealth occurs before adjusting his consumption. As a consequence, the consumption based capital asset pricing model fails to hold. Nevertheless, it is shown that the standard, one factor, market portfolio based capital asset pricing model does hold in this environment. It is shown that the optimal durable level is characterized by three numbers (not random variables), say x, y, and z (where x
Author: Youri Kabanov
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We consider a consumption-investment optimization problem for the Kabanov model when the proportional transaction costs rate is constant and the prices are modeled by a Lévy process. We naturally extend the preliminary work of [4] to portfolio processes that are only supposed to be làdlàg. This allows to suitably rebalance portfolio processes which jumps induced by the Lévy process and identify an optimal strategy in the two dimensional case.
Author: Chang Mo Ahn
Publisher:
ISBN:
Category : Stocks
Languages : en
Pages : 456
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Book Description
Author: Jia-An Yan
Publisher: Springer
ISBN: 9811316570
Category : Mathematics
Languages : en
Pages : 403
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Book Description
This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.
Author: Matheus R. Grasselli
Publisher: World Scientific
ISBN: 9814407887
Category : Business & Economics
Languages : en
Pages : 598
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Book Description
This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.
Author: Masanobu Taniguchi
Publisher: CRC Press
ISBN: 1351643622
Category : Mathematics
Languages : en
Pages : 455
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Book Description
The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered. This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.
Author: Bernard Dumas
Publisher:
ISBN:
Category :
Languages : en
Pages : 42
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Book Description
