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Optimal Investment And Consumption Portfolio Choice Problem For Assets Modeled By Levy Processes
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Book Synopsis Optimal Investment and Consumption Portfolio Choice Problem for Assets Modeled by Levy Processes by : Ryan G. Sankarpersad
Download or read book Optimal Investment and Consumption Portfolio Choice Problem for Assets Modeled by Levy Processes written by Ryan G. Sankarpersad and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Consumption and Portfolio Decisions when Expected Returns are Time Varying by : John Y. Campbell
Download or read book Consumption and Portfolio Decisions when Expected Returns are Time Varying written by John Y. Campbell and published by . This book was released on 1996 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods by : Sanford J. Grossman
Download or read book Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods written by Sanford J. Grossman and published by . This book was released on 1987 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Consumption-Investment Optimization Problem in a Lévy Financial Model with Transaction Costs by : Youri Kabanov
Download or read book Consumption-Investment Optimization Problem in a Lévy Financial Model with Transaction Costs written by Youri Kabanov and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Portfolio Selection and Asset Pricing Under Variable Time Preference by : Chang Mo Ahn
Download or read book Portfolio Selection and Asset Pricing Under Variable Time Preference written by Chang Mo Ahn and published by . This book was released on 1985 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Stochastic Finance by : Jia-An Yan
Download or read book Introduction to Stochastic Finance written by Jia-An Yan and published by Springer. This book was released on 2018-10-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Essays on Pricing and Portfolio Choice in Incomplete Markets by : Ti Zhou
Download or read book Essays on Pricing and Portfolio Choice in Incomplete Markets written by Ti Zhou and published by . This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is a contribution to the pricing and portfolio choice theory in incomplete markets. It consists of three self-contained but interlinked essays. In the first essay, we present a utility-based methodology for the valuation and the risk management of mortgage-backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded pre-payment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools. In the second essay, using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth processes in an incomplete non-Markovian market with asset prices modelled as Ito processes. The methodology allows for measuring the investment performance in terms of a benchmark and alter-native market views. In the last essay, we extend the forward investment performance approach to study the optimal portfolio choice problem in an incomplete market driven by jump processes. The asset price is modelled by a one-dimensional Lévy-Itô process. We prove the existence of a forward performance process by restricting the local risk tolerance functions to be time-independent and linear in wealth. This yields only three types of performance measurement criteria, namely, exponential, power and logarithmic. The optimal portfolios are constructed via stochastic feedback controls under these criteria.
Book Synopsis Finance at Fields by : Matheus R. Grasselli
Download or read book Finance at Fields written by Matheus R. Grasselli and published by World Scientific. This book was released on 2013 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Statistical Portfolio Estimation by : Masanobu Taniguchi
Download or read book Statistical Portfolio Estimation written by Masanobu Taniguchi and published by CRC Press. This book was released on 2017-09-01 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimal Portfolios written by Ralf Korn and published by World Scientific. This book was released on 1997 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.
Book Synopsis An Exact Solution to the Portfolio Choice Problem Under Transactions Costs by : Bernard Dumas
Download or read book An Exact Solution to the Portfolio Choice Problem Under Transactions Costs written by Bernard Dumas and published by . This book was released on 1989 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Portfolio Selection in Stochastic Environment by : Karan Thagunna
Download or read book Optimal Portfolio Selection in Stochastic Environment written by Karan Thagunna and published by LAP Lambert Academic Publishing. This book was released on 2010-04 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we consider a particular case of an optimal consumption and portfolio selection problem for an innitely lived investor whose consumption rate process is subject to downside constraint. We also suppose that the wealth dynamics is composed of three assets (i) riskless assets (ii) risky assets (iii) hedge assets. We consider the investor's wealth process, interpreted in the sense of the It DEGREESo integral.Our work aims to find the optimal policies which maximize the expected discount utility function.Furthermore, we obtain the optimal policies in an explicit form for the log utility function which is a special case of the general utility (CRRA) function, using the martingale method and applying the Legendre transform formula and the Feynman-kac formula. We derive some numerical results for the optimal policies and compare the results with the classical Merton's result evaluated for an innite horizon case.
Book Synopsis Advanced Financial Modelling by : Hansjörg Albrecher
Download or read book Advanced Financial Modelling written by Hansjörg Albrecher and published by Walter de Gruyter. This book was released on 2009 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a a ~Special Semester on Stochastics with Emphasis on Financea (TM) that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria
Book Synopsis Portfolio Choice and Asset Pricing with Nontraded Assets by : Lars E. O. Svensson
Download or read book Portfolio Choice and Asset Pricing with Nontraded Assets written by Lars E. O. Svensson and published by . This book was released on 1988 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines portfolio choice and asset pricing when some assets are nontraded, for instance when a country cannot trade claims to its output on world capital markets, when a government cannot trade claims to future tax revenues, or when an individual cannot trade claims to his future wages. The close relation between portfolio choice with and implicit pricing of nontraded assets is emphasized. A variant of Cox, Ingersoll and Ross's Fundamental Valuation Equation is derived and used to interpret the optimal portfolio. Explicit solutions are presented to the portfolio and pricing problem for some special cases, including when income from the nontraded assets is a diffusion process, not spanned by traded assets, and affected by a state variable.
Book Synopsis Handbook of the Fundamentals of Financial Decision Making by : Leonard C. MacLean
Download or read book Handbook of the Fundamentals of Financial Decision Making written by Leonard C. MacLean and published by World Scientific. This book was released on 2013 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook in two parts covers key topics of the theory of financial decision making. Some of the papers discuss real applications or case studies as well. There are a number of new papers that have never been published before especially in Part II.Part I is concerned with Decision Making Under Uncertainty. This includes subsections on Arbitrage, Utility Theory, Risk Aversion and Static Portfolio Theory, and Stochastic Dominance. Part II is concerned with Dynamic Modeling that is the transition for static decision making to multiperiod decision making. The analysis starts with Risk Measures and then discusses Dynamic Portfolio Theory, Tactical Asset Allocation and Asset-Liability Management Using Utility and Goal Based Consumption-Investment Decision Models.A comprehensive set of problems both computational and review and mind expanding with many unsolved problems are in an accompanying problems book. The handbook plus the book of problems form a very strong set of materials for PhD and Masters courses both as the main or as supplementary text in finance theory, financial decision making and portfolio theory. For researchers, it is a valuable resource being an up to date treatment of topics in the classic books on these topics by Johnathan Ingersoll in 1988, and William Ziemba and Raymond Vickson in 1975 (updated 2 nd edition published in 2006).
Book Synopsis Advances in Econometrics, Operational Research, Data Science and Actuarial Studies by : M. Kenan Terzioğlu
Download or read book Advances in Econometrics, Operational Research, Data Science and Actuarial Studies written by M. Kenan Terzioğlu and published by Springer Nature. This book was released on 2022-01-17 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents techniques and theories drawn from mathematics, statistics, computer science, and information science to analyze problems in business, economics, finance, insurance, and related fields. The authors present proposals for solutions to common problems in related fields. To this end, they are showing the use of mathematical, statistical, and actuarial modeling, and concepts from data science to construct and apply appropriate models with real-life data, and employ the design and implementation of computer algorithms to evaluate decision-making processes. This book is unique as it associates data science - data-scientists coming from different backgrounds - with some basic and advanced concepts and tools used in econometrics, operational research, and actuarial sciences. It, therefore, is a must-read for scholars, students, and practitioners interested in a better understanding of the techniques and theories of these fields.
Book Synopsis An Intertemporal Model of Consumption and Portfolio Allocation by : Hans Andersson
Download or read book An Intertemporal Model of Consumption and Portfolio Allocation written by Hans Andersson and published by . This book was released on 1995 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
