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Optimal Lifetime Consumption Portfolio Strategies Under Trading Constraints And Generalized Recursive Preferences
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Book Synopsis Optimal Lifetime Consumption-Portfolio Strategies Under Trading Constraints and Generalized Recursive Preferences by : Mark D. Schroder
Download or read book Optimal Lifetime Consumption-Portfolio Strategies Under Trading Constraints and Generalized Recursive Preferences written by Mark D. Schroder and published by . This book was released on 2006 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based on a preference-independent notion of constrained state pricing. For homothetic generalized recursive utility, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained BSDE. Incomplete market solutions are related to complete markets solutions with modified risk aversion towards non-marketed risk. Methodologically, we develop the utility gradient approach, but for the homothetic case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the BSDE characterizing the solution reduces to a system of Riccati equations.
Book Synopsis Lifetime Consumption-Portfolio Choice Under Trading Constraints, Recursive Preferences and Nontradeable Income by : Mark D. Schroder
Download or read book Lifetime Consumption-Portfolio Choice Under Trading Constraints, Recursive Preferences and Nontradeable Income written by Mark D. Schroder and published by . This book was released on 2003 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, a possibly nontradeable income stream, and convex constraints on the vector of market values of financial positions. (The setting extends Schroder and Skiadas, 2002, where the endowment is assumed tradeable and constraints are imposed in terms of wealth proportions.) For any utility function with a supergradient density, we develop the first-order conditions of optimality, a side-product being the characterization of a constrained notion of state-pricing. The methodology is applied to generalized continuous-time recursive utility, allowing for first and second-order risk-aversion that can depend on the risk source, reflecting the source's quot;ambiguity.quot; Within this class, we isolate a more tractable formulation in which preferences exhibit no wealth effects (an example being time-additive expected discounted exponential utility), and there is unrestricted trading in a money market and a suitably defined consol bond. In this case, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained backward stochastic differential equation (BSDE), which in a Markovian setting maps to a PDE. Methodologically, we develop the utility gradient approach, but for the wealth-invariant case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the PDE characterizing the solution simplifies to a system of ordinary differential equations (of the Riccati type).
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 Asset Pricing Theory by : Costis Skiadas
Download or read book Asset Pricing Theory written by Costis Skiadas and published by Princeton University Press. This book was released on 2009-02-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asset Pricing Theory is an advanced textbook for doctoral students and researchers that offers a modern introduction to the theoretical and methodological foundations of competitive asset pricing. Costis Skiadas develops in depth the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, but with emphasis on geometric and martingale methods that facilitate an effortless transition to the more advanced continuous-time theory. Among the book's many innovations are its use of recursive utility as the benchmark representation of dynamic preferences, and an associated theory of equilibrium pricing and optimal portfolio choice that goes beyond the existing literature. Asset Pricing Theory is complete with extensive exercises at the end of every chapter and comprehensive mathematical appendixes, making this book a self-contained resource for graduate students and academic researchers, as well as mathematically sophisticated practitioners seeking a deeper understanding of concepts and methods on which practical models are built. Covers in depth the modern theoretical foundations of competitive asset pricing and consumption/portfolio choice Uses recursive utility as the benchmark preference representation in dynamic settings Sets the foundations for advanced modeling using geometric arguments and martingale methodology Features self-contained mathematical appendixes Includes extensive end-of-chapter exercises
Book Synopsis Advanced Asset Pricing Theory by : Ma Chenghu
Download or read book Advanced Asset Pricing Theory written by Ma Chenghu and published by World Scientific Publishing Company. This book was released on 2011-01-03 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction of modern asset pricing theory with equal treatments for both discrete-time and continuous-time modeling. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework.The analyses and coverage are up to date, comprehensive and in-depth. Topics include microeconomic foundation of asset pricing theory, the no-arbitrage principle and fundamental theorem, risk measurement and risk management, sequential portfolio choice, equity premium decomposition, option pricing, bond pricing and term structure of interest rates. The merits and limitations are expounded with respect to allocation and information market efficiency, along with the classical expectations hypothesis concerning the information content of yield curve and bond prices. Efforts are also made towards the resolution of several well-documented puzzles in empirical finance, which include the equity premium puzzle, the risk free rate puzzle, and the money-ness bias phenomenon of Black-Scholes option pricing model.The theory is self-contained and unified in presentation. The inclusion of proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory makes an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The explanations are detailed enough to capture the interest of those curious readers, and complete enough to provide necessary background material needed to explore further the subject and research literature.
Book Synopsis Consumption-portfolio Choice with Preferences for Cash by : Holger Kraft
Download or read book Consumption-portfolio Choice with Preferences for Cash written by Holger Kraft and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.
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 Handbook of Computational Economics by : Karl Schmedders
Download or read book Handbook of Computational Economics written by Karl Schmedders and published by Newnes. This book was released on 2013-12-31 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. Samples different styles and approaches, reflecting the breadth of computational economics as practiced today Focuses on problems with few well-developed solutions in the literature of other disciplines Emphasizes the potential for increasing the value of computational modeling in economics
Book Synopsis Optimal Consumption and Investment with Epstein-Zin Recursive Utility by : Holger Kraft
Download or read book Optimal Consumption and Investment with Epstein-Zin Recursive Utility written by Holger Kraft and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to compute both indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.
Book Synopsis Lifetime Investment and Consumption with Recursive Preferences and Small Transaction Costs by : Yaroslav Melnyk
Download or read book Lifetime Investment and Consumption with Recursive Preferences and Small Transaction Costs written by Yaroslav Melnyk and published by . This book was released on 2017 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article investigates the effects of small proportional transaction costs on lifetime consumption and portfolio decisions. The extant literature has focused on agents with additive utility; here, we argue that this is essentially without loss of generality at the leading order for small costs. To shed light on the effects of alternative risk preferences, we in turn perform a higher-order analysis for the archetype of non-additive preferences - the isoelastic recursive utilities proposed by Epstein and Zin.
Book Synopsis Can Standard Preferences Explain the Prices of Out of the Money S&P 500 Put Options by : Luca Benzoni
Download or read book Can Standard Preferences Explain the Prices of Out of the Money S&P 500 Put Options written by Luca Benzoni and published by . This book was released on 2005 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S & P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S & P 500 put options have become 'expensive' relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has 'standard preferences' and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the 'volatility smirk' can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.
Book Synopsis Time-Varying Margin Requirements and Optimal Portfolio Choice by : Oleg Rytchkov
Download or read book Time-Varying Margin Requirements and Optimal Portfolio Choice written by Oleg Rytchkov and published by . This book was released on 2016 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the optimal consumption and portfolio problem of an investor with recursive preferences who is subject to time-varying margin requirements. The level of the requirements at each moment is determined by contemporaneous volatility of returns, which is stochastic and may have jumps. I show that nonstandard hedging demand produced by margin requirements increases with their persistence and volatility. However, for realistic values of parameters the hedging demand is small even in the presence of jumps and contemporaneous jumps in prices have a much stronger effect on optimal portfolio than jumps in constraints.
Download or read book Australian Economic Papers written by and published by . This book was released on 2005 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Working Paper Series written by and published by . This book was released on 2003 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences by : Claus Munk
Download or read book Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences written by Claus Munk and published by . This book was released on 2002 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the dynamic consumption and portfolio choice of an investor who has habit formation in preferences and access to a complete financial market. For general, possibly non-Markov, dynamics of market prices, we provide an exact characterization of the optimal behavior in terms of two relatively simple and intuitively interpretable stochastic processes. We study in more detail the optimal strategies in two concrete examples of time-varying investment opportunities. Firstly, we derive a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns. Secondly, with Cox-Ingersoll-Ross interest rate dynamics we can express the optimal strategies in terms of the solution to a partial differential equation, which has an explicit solution for time-additive preferences, but not with habit formation. Our numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level. The implications of habit persistence in models with labor income are also addressed.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Strategic Asset Allocation by : John Y. Campbell
Download or read book Strategic Asset Allocation written by John Y. Campbell and published by OUP Oxford. This book was released on 2002-01-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.
