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Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets

2012-08-27 Business & Economics
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Release : 2012-08-27
Genre : Business & Economics
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Book Rating : 412/5 ( reviews)

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Book Synopsis Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets by : Holger Kraft

Download or read book Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets written by Holger Kraft. This book was released on 2012-08-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Portfolios with Stochastic Short Rate

2005
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Release : 2005
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Book Synopsis Optimal Portfolios with Stochastic Short Rate by : Holger Kraft

Download or read book Optimal Portfolios with Stochastic Short Rate written by Holger Kraft. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to highlight some of the problems occuring when one leaves the usual path of portfolio problems with Gaussian interest rates and bounded market price of risk. We solve several portfolio problems for different specifications of the short rate and the market price of risk. More precisely, we consider a Gaussian model, the Cox-Ingersoll-Ross model, and squared Gaussian as well as lognormal specifications of the short rate. Even for the seemingly innocent Gaussian model, the problem may explode in a certain sense if the market price of risk is unbounded. From an economic point of view, in this case the model does not exhibit a partial equilibrium indicating that, for instants, the time-preferences of the investor are not properly modeled. This problem can be overcome by introducing short rate depending time preferences. Above all, we strongly emphasize that it is not straightforward to generalize the existing results on continuous-time portfolio optimization to the case of a Non-Gaussian stochastic short rate or to a Gaussian term structure with unbounded market price of risk.

Optimal Portfolios

1997 Business & Economics
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Release : 1997
Genre : Business & Economics
Kind : eBook
Book Rating : 347/5 ( reviews)

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Book Synopsis Optimal Portfolios by : Ralf Korn

Download or read book Optimal Portfolios written by Ralf Korn. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.

On Optimal Portfolio Choice Under Stochastic Interest Rates

2010
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Release : 2010
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Book Synopsis On Optimal Portfolio Choice Under Stochastic Interest Rates by : Abraham Lioui

Download or read book On Optimal Portfolio Choice Under Stochastic Interest Rates written by Abraham Lioui. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: In an economy where interest rates and stock price changes follow fairly general stochastic processes, we analyse the portfolio problem of an expected utility investor. When the investment opportunity set is driven by an arbitrary number of state variables, the optimal portfolio strategy is known to contain a speculative element and Merton-Breeden hedging terms against the fluctuations of each and every state variable. While the first component is well identified and easy to work out, the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics. Using a new decomposition of the optimal wealth, we show that the optimal strategy can be simplified to include, in addition to the speculative component, only two Merton-Breeden type hedging elements, however large is the number of state variables. The first one is associated with interest rate risk and the second one with the risk brought about by the co-movements of the spot interest rate and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Moreover, the investor's horizon is shown explicitly to play a crucial role in the optimal strategy design, in sharp contrast with the traditional decomposition.

Stochastic Portfolio Theory

2013-04-17 Business & Economics
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Release : 2013-04-17
Genre : Business & Economics
Kind : eBook
Book Rating : 991/5 ( reviews)

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Book Synopsis Stochastic Portfolio Theory by : E. Robert Fernholz

Download or read book Stochastic Portfolio Theory written by E. Robert Fernholz. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.

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