Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance

ISBN-13: 9783642055676 / Angielski / Miękka / 2010 / 198 str.

Alexandre C. Ziegler

Opis

Continuous-time finance was developed in the late sixties and early seventies by R. C. Merton. Over the years, due to its elegance and analytical conve nience, the continuous-time paradigm has become the standard tool of anal ysis in portfolio theory and asset pricing. However, and probably because it was developed hand in hand with option pricing, in which investors' expecta tions were thought not to matter, continuous-time finance has for a long time almost entirely neglected investors' beliefs. More recently, the development of martingale pricing techniques, in which expectations playa dominant role, and the blurring boundary between those methods and the original methods of continuous-time finance based on the Ito calculus, have allowed expecta tions to regain their central role in finance. The habilitation thesis of Professor Alexandre Ziegler is entirely devoted to the role of expectations in continuous-time finance. After a brief review of the literature, the author analyzes the consequences of incomplete informa tion and heterogeneous beliefs for optimal portfolio and consumption choice and equilibrium asset pricing. Relaxing the assumption that investors can ob serve expected dividend growth perfectly, the author shows that incomplete information affects stock prices and their dynamics, thus providing a potential explanation for the asset price bubble of the late 1990s. He also demonstrates how the presence of heterogeneous beliefs among investors affects their opti mal portfolios and their optimal consumption patterns."

Recenzje

From the reviews of the first edition:

"The book is mainly addressed to researchers and graduate students in the fields of economics or finance. However, interested practitioners may also be counted to its target audience. ... the book presents an interesting source for those readers interested in the interplay of (micro-) economics and finance, ie. of incomplete information, heterogeneous beliefs and continuous-time financial models." (Klaus Schürger, Zentralblatt MATH, Vol. 1074, 2005)

Spis treści

1 Incomplete Information: An Overview.- 1.1 Introduction.- 1.2 Portfolio Choice.- 1.2.1 Gennotte’s Model.- 1.2.2 The Inference Process.- 1.2.3 Optimal Portfolio Choice.- 1.2.4 An Example.- 1.2.5 The Short Interest Rate.- 1.3 The Term Structure of Interest Rates.- 1.3.1 Dothan and Feldman’s Models.- 1.3.2 A Characterization of the Term Structure.- 1.4 Equilibrium Asset Pricing.- 1.4.1 Honda’s Model.- 1.4.2 The Equilibrium Price Process.- 1.5 Conclusion and Outlook.- 2 The Impact of Incomplete Information on Utility, Prices, and Interest Rates.- 2.1 Introduction.- 2.2 The Model.- 2.3 Equilibrium.- 2.3.1 The Equilibrium Expected Lifetime Utility.- 2.3.2 The Equilibrium Price.- 2.3.3 The Equilibrium Interest Rate.- 2.4 Logarithmic Utility.- 2.4.1 The Equilibrium Expected Lifetime Utility.- 2.4.2 The Equilibrium Price.- 2.4.3 The Equilibrium Interest Rate.- 2.5 Power Utility.- 2.5.1 The Equilibrium Expected Lifetime Utility.- 2.5.2 The Equilibrium Price.- 2.5.3 The Equilibrium Interest Rate.- 2.5.4 Hedging Demand and the Equilibrium Price of Estimation Risk.- 2.6 Information, Utility, Prices, and Interest Rates: A Synthesis.- 2.6.1 Expected Lifetime Utility.- 2.6.2 Share Prices.- 2.6.3 Interest Rates.- 2.7 Time-Varying Parameters.- 2.7.1 The Equilibrium Expected Lifetime Utility.- 2.7.2 The Equilibrium Price.- 2.7.3 The Equilibrium Interest Rate.- 2.8 Conclusion.- 3 Optimal Portfolio Choice Under Heterogeneous Beliefs.- 3.1 Introduction.- 3.2 The Model.- 3.3 The Deviant Agent’s Problem.- 3.4 Optimal Portfolio Choice.- 3.5 An Example.- 3.6 Conclusion.- 4 Optimal Consumption Under Heterogeneous Beliefs.- 4.1 Introduction.- 4.2 The Cox-Huang Methodology.- 4.3 Heterogeneous Beliefs.- 4.4 An Example.- 4.4.1 The Model.- 4.4.2 Optimal Consumption Patterns Under Heterogeneous Beliefs.- 4.4.3 An Algebraic Solution.- 4.4.4 The Effect of the Time Horizon.- 4.5 Portfolios and Consumption: A Synthesis.- 4.6 Conclusion.- 5 Equilibrium Asset Pricing Under Heterogeneous Beliefs.- 5.1 Introduction.- 5.2 The Model.- 5.3 Equilibrium Consumption.- 5.4 Equilibrium Prices.- 5.4.1 The Equilibrium State-Price Density.- 5.4.2 The Equilibrium Short Rate.- 5.4.3 The Equilibrium Yield Curve.- 5.4.4 The Equilibrium Share Price.- 5.4.5 Equilibrium Option Prices and the “Smile Effect”.- 5.5 Implied Risk Aversion.- 5.6 Conclusion.- 6 Costly Information, Imperfect Learning, and Information Aggregation.- 6.1 Introduction.- 6.2 The Model.- 6.2.1 The Economy.- 6.2.2 The Inference Process: Imperfect Learning.- 6.3 Portfolio Choice under Costly Information.- 6.3.1 The Agent’s Problem.- 6.3.2 The Agent’s Optimal Investment and Research Policy.- 6.3.3 Determinants of the Demand for Information.- 6.3.4 Diversification and Information Costs.- 6.4 Equilibrium Asset Pricing.- 6.5 Information Aggregation and the Equity Premium.- 6.6 Conclusion.- 7 Summary and Conclusion.- C The Short Rate Under Heterogeneous Beliefs.- References.- List of Figures.- List of Tables.- List of Symbols.