Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets
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Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets: (540 Lecture Notes in Economics and Mathematical Systems)

Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets: (540 Lecture Notes in Economics and Mathematical Systems)


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About the Book

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.

Table of Contents:
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.


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Product Details
  • ISBN-13: 9783540212300
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 174
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 3540212302
  • Publisher Date: 13 Apr 2004
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 540 Lecture Notes in Economics and Mathematical Systems


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Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets: (540 Lecture Notes in Economics and Mathematical Systems)
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