Portfolio Optimization With Risk Constraints In The View Of Stochastic Interest Rates
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Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets
| Author | : Holger Kraft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 178 |
| Release | : 2012-08-27 |
| Genre | : Business & Economics |
| ISBN | : 3642170412 |
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.
Interest Rate Uncertainty and Strategic Asset Allocation with Borrowing and Short Sales Constraints
| Author | : Carsten Sørensen |
| Publisher | : |
| Total Pages | : 28 |
| Release | : 2007 |
| Genre | : |
| ISBN | : |
The paper provides the solution to a dynamic portfolio problem of an investor who faces borrowing and short sales constraints in a setting with stochastic interest rates. The multi-asset dynamic problem is reduced to a constrained quadratic optimization problem which is similar to the well-known problem studied in static mean-variance portfolio theory. As an example and illustration of the general results, the paper focuses on the closed-form portfolio solution of a borrowing constrained long-term investor who cannot perfectly replicate very long-term real bonds and instead uses other securities (e.g. stocks) to hedge real interest risk. The efficiency loss due to, e.g., such a borrowing constraint is addressed.
Optimal Portfolios
| Author | : Ralf Korn |
| Publisher | : World Scientific |
| Total Pages | : 352 |
| Release | : 1997 |
| Genre | : Business & Economics |
| ISBN | : 9812385347 |
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.
Stochastic Portfolio Theory
| Author | : E. Robert Fernholz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2002-04-12 |
| Genre | : Business & Economics |
| ISBN | : 9780387954059 |
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.
Dynamic Asset Allocation Under VAR Constraint with Stochastic Interest Rates
| Author | : Donatien Hainaut |
| Publisher | : |
| Total Pages | : 20 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
This paper addresses the problem of dynamic asset allocation under a bounded shortfall risk in a market composed of three assets: cash, stocks and a zero coupon bond. The dynamics of the instantaneous short rates is driven by a Hull and White model. In this setting, we determine and compare optimal investment strategies maximizing the CRRA utility of terminal wealth with and without value at risk constraint.
Optimal Portfolios with Stochastic Short Rate
| Author | : Holger Kraft |
| Publisher | : |
| Total Pages | : 32 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
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.
Linear and Mixed Integer Programming for Portfolio Optimization
| Author | : Renata Mansini |
| Publisher | : Springer |
| Total Pages | : 131 |
| Release | : 2015-06-10 |
| Genre | : Business & Economics |
| ISBN | : 3319184822 |
This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.
Dynamic Asset Allocation with Stochastic Income and Interest Rates
| Author | : Claus Munk |
| Publisher | : |
| Total Pages | : 63 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
We investigate the optimal investment and consumption choice of individual investors with uncertain future labor income operating in a financial market with stochastic interest rates. Since the present value of the individual's future income is a main determinant of the optimal behavior and this present value depends heavily on the interest rate dynamics, the joint stochastics of income and interest rates will have consequences beyond the separate effects of stochastic income and stochastic interest rates. We study both the case where income risk is spanned and there are no portfolio constraints and the case with non-spanned income risk and a constraint ruling out borrowing against future income. For the spanned, unconstrained problem we study a special case in which we obtain closed-form expressions for the optimal policies. For the unspanned, constrained problem we implement a numerical solution technique and compare the solutions to the spanned, unconstrained problem. We also allow for typical life-cycle variations in labor income.
Modern Portfolio Optimization with NuOPT™, S-PLUS®, and S+Bayes™
| Author | : Bernd Scherer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 442 |
| Release | : 2005-05-03 |
| Genre | : Business & Economics |
| ISBN | : 9780387210162 |
Portfolio optimization and construction methodologies have become an critical ingredient of asset and fund management, while at same time portfolio risk assesment has become an essential ingredient in risk management.
