Holger Kraft

Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets

• Broschiertes Buch

Produktbeschreibung

The continuous-time portfolio problem consists of finding the optimal investment strategy of an investor. In the classical Merton problem the investor can allocate his funds to a riskless savings account and risky assets. However, to get explicit results, it is assumed that the interest rates are deterministic and that the assets are default free. In this monograph both assumptions are weakened: The author analyzes and solves portfolio problems with stochastic interest rates and with defaultable assets. Besides, he briefly discusses how portfolio problems with foreign assets can be handled. The focus of the monograph is twofold: On the one hand, the economical problems are carefully explained, on the other hand their formal solution is rigorously presented. For this reason the text should be of interest to researchers with a Finance background as well as to researchers with a more formal background who would like to see how mathematics is applied to portfolio theory.

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This thesis summarizes most of my recent research in the field of portfolio optimization. The main topics which I have addressed are portfolio problems with stochastic interest rates and portfolio problems with defaultable assets. The starting point for my research was the paper "A stochastic control ap proach to portfolio problems with stochastic interest rates" (jointly with Ralf Korn), in which we solved portfolio problems given a Vasicek term structure of the short rate. Having considered the Vasicek model, it was obvious that I should analyze portfolio problems where the interest rate dynamics are gov erned by other common short rate models. The relevant results are presented in Chapter 2. The second main issue concerns portfolio problems with default able assets modeled in a firm value framework. Since the assets of a firm then correspond to contingent claims on firm value, I searched for a way to easily deal with such claims in portfolio problems. For this reason, I developed the elasticity approach to portfolio optimization which is presented in Chapter 3. However, this way of tackling portfolio problems is not restricted to portfolio problems with default able assets only, but it provides a general framework allowing for a compact formulation of portfolio problems even if interest rates are stochastic.

Produktdetails

• Lecture Notes in Economics and Mathematical Systems 540
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-21230-0
• Softcover reprint of the original 1st ed. 2004
• Seitenzahl: 184
• Erscheinungstermin: 13. April 2004
• Englisch
• Abmessung: 235mm x 155mm x 11mm
• Gewicht: 288g
• ISBN-13: 9783540212300
• ISBN-10: 3540212302
• Artikelnr.: 12687081

Autorenporträt

Holger Kraft, Fraunhofer Institut, Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany

Inhaltsangabe

1 Preliminaries from Stochastics.- 1.1 Stochastic Differential Equations.- 1.2 Stochastic Optimal Control.- 2 Optimal Portfolios with Stochastic Interest Rates.- 2.1 Introduction.- 2.2 Ho-Lee and Vasicek Model.- 2.3 Dothan and Black-Karasinski Model.- 2.4 Cox-Ingersoll-Ross Model.- 2.5 Widening the Investment Universe.- 2.6 Conclusion.- 3 Elasticity Approach to Portfolio Optimization.- 3.1 Introduction.- 3.2 Elasticity in Portfolio Optimization.- 3.3 Duration in Portfolio Optimization.- 3.4 Conclusion.- 3.5 Appendix.- 4 Barrier Derivatives with Curved Boundaries.- 4.1 Introduction.- 4.2 Bjork's Result.- 4.3 Deterministic Exponential Boundaries.- 4.4 Discounted Barrier and Gaussian Interest Rates.- 4.5 Application: Pricing of Defaultable Bonds.- 4.6 Conclusion.- 5 Optimal Portfolios with Defaultable Assets - A Firm Value Approach.- 5.1 Introduction.- 5.2 The Unconstrained Case.- 5.3 From the Unconstrained to the Constrained Case.- 5.4 The Constrained Case.- 5.5 Conclusion.- References.- Abbreviations.- Notations.