9

32

 

Princeton University Press (Visit publisher website)

2001

English

 

 

 

Advanced

 

 

Investment management, quantitative analysis, portfolio theory, estimation, stochastic processes, optimization techniques, stochastic control, Hamilton-Jacobi-Bellman (HJB) equation, Merton`s optimal consumption and investment problem, relative risk aversion, hyperbolic absolute risk averse, infinite horizon case, martingale formulation/solution of Merton`s problem, utility-gradient approach

 

Excerpt from book - This chapter presents basic results on optimal portfolio and consumption choice, first using dynamic programming, then using general martingale and utility-gradient methods. We begin with a review of the Hamilton-Jacobi-Bellman equation for stochastic control, and then apply it to Merton’s problem of optimal consumption and portfolio choice in finite- and infinite-horizon settings. Then, exploiting the properties of equivalent martingale measures from Chapter 6, Merton’s problem is solved once again in a non-Markovian setting. Finally, we turn to the general utility-gradient approach from Chapter 2, and show that it coincides with the approach of equivalent martingale measures.

 

A Stochastic Control
B Merton’s Problem
C Solution to Merton’s Problem
D The Infinite-Horizon Case
E The Martingale Formulation
F Martingale Solution
G A Generalization
H The Utility-Gradient Approach
Exercises
Notes

 

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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 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. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.