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Portfolio Selection and Asset Pricing

Portfolio Selection and Asset Pricing
Author: Shouyang Wang
Publisher: Springer Science & Business Media
Total Pages: 260
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642559344

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In our daily life, almost every family owns a portfolio of assets. This portfolio could contain real assets such as a car, or a house, as well as financial assets such as stocks, bonds or futures. Portfolio theory deals with how to form a satisfied portfolio among an enormous number of assets. Originally proposed by H. Markowtiz in 1952, the mean-variance methodology for portfolio optimization has been central to the research activities in this area and has served as a basis for the development of modem financial theory during the past four decades. Follow-on work with this approach has born much fruit for this field of study. Among all those research fruits, the most important is the capital asset pricing model (CAPM) proposed by Sharpe in 1964. This model greatly simplifies the input for portfolio selection and makes the mean-variance methodology into a practical application. Consequently, lots of models were proposed to price the capital assets. In this book, some of the most important progresses in portfolio theory are surveyed and a few new models for portfolio selection are presented. Models for asset pricing are illustrated and the empirical tests of CAPM for China's stock markets are made. The first chapter surveys ideas and principles of modeling the investment decision process of economic agents. It starts with the Markowitz criteria of formulating return and risk as mean and variance and then looks into other related criteria which are based on probability assumptions on future prices of securities.


Dynamic Asset Pricing Theory

Dynamic Asset Pricing Theory
Author: Darrell Duffie
Publisher: Princeton University Press
Total Pages: 488
Release: 2010-01-27
Genre: Business & Economics
ISBN: 1400829208

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This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.


Financial Derivatives

Financial Derivatives
Author: Jamil Baz
Publisher: Cambridge University Press
Total Pages: 358
Release: 2004-01-12
Genre: Business & Economics
ISBN: 1107268737

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This book offers a complete, succinct account of the principles of financial derivatives pricing. The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Ito's lemma are discussed heuristically. The second chapter develops generic pricing techniques for assets and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives. The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discusses factor models and term structure consistent models. The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions such as mean-reverting processes and jump processes and discusses related tools of stochastic calculus such as Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.


The Valuation of Contingent Claims Under Portfolio Constraints

The Valuation of Contingent Claims Under Portfolio Constraints
Author: Claus Munk
Publisher:
Total Pages: 42
Release: 2001
Genre:
ISBN:

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With constrained portfolios contingent claims do generally not have a unique price that rules out arbitrage opportunities. Earlier studies have demonstrated that, when there are no constraints on the hedge portfolio, a no-arbitrage price interval for any contingent claim exists. I consider the more realistic case where the constraints are imposed on the total portfolio of each investor and define reservation buying and selling prices for contingent claims. I show how these reservation prices can be computed numerically and study two simple examples in which the reservation prices and the corresponding hedging strategies are compared to the Black-Scholes setting. Such computations are highly relevant, e.g., for the valuation of real options.


Arbitrage Pricing of Contingent Claims

Arbitrage Pricing of Contingent Claims
Author: Sigrid Müller
Publisher: Springer Science & Business Media
Total Pages: 160
Release: 2013-03-13
Genre: Law
ISBN: 3642465609

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Hedging American Contingent Claims with Constrained Portfolios

Hedging American Contingent Claims with Constrained Portfolios
Author: Ioannis Karatzas
Publisher:
Total Pages:
Release: 1998
Genre:
ISBN:

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The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending. In the unconstrained case, the classical theory provides a single arbitrage-free price $u_0$; this is expressed as the supremum, over all stopping times, of the claim's expected discounted value under the equivalent martingale measure. In the presence of constraints, $ {u_0 }$ is replaced by an entire interval $[h_{ rm low}, h_{ rm up}]$ of arbitrage-free prices, with endpoints characterized as $h_{ rm low} = inf_{ nu in{ cal D}}u_ nu, h_{ rm up} = sup_{ nu in{ cal D}} u_ nu$. Here $u_ nu$ is the analogue of $u_0$, the arbitrage-free price with unconstrained portfolios, in an auxiliary market model ${ cal M}_ nu$; and the family $ {{ calM}_ nu }_{ nu in{ cal D}}$ is suitably chosen, to contain the original model and to reflect the constraints on portfolios. For several such constraints, explicit computations of the endpoints are carried out in the case of the American call-option. The analysis involves novel results in martingale theory (including simultaneous Doob Meyer decompositions), optimal stopping and stochastic control problems, stochastic games, and uses tools from convex analysis.


Hedging Contingent Claims with Constrained Portfolios and Nonlinear Wealth Dynamics

Hedging Contingent Claims with Constrained Portfolios and Nonlinear Wealth Dynamics
Author: Dirk Ebmeyer
Publisher:
Total Pages: 23
Release: 2007
Genre:
ISBN:

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The purpose of this paper is to characterize the cost of super-replicating a contingent claim in a dynamic stochastic securities market under constraints. The dynamic market under consideration will allow for two different types of trading frictions: convex constraints on the portfolio processes describing the amount of money invested in the securities as well as nonlinearities in the stochastic differential equation which drives the evolution of the investors wealth. Besides a characterization of the upper hedging price of a contingent claim using stochastic control theory, the main result of this paper is an existence result for a hedging strategy for a given contingent claim in case agents only face nonlinearities in their wealth process.