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Iterative Solvers for Portfolio Optimization
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In this paper we propose iterative solvers for portfolio optimization in a two dimensional domain. To put the modeled equations into practice we provide Jacobi and Gauss-Seidal algorithms. In order to improve the efficiency of portfolio optimization iterative solvers we study the convergence rate and introduce successive over relaxation scheme to the developed algorithms. Further to overcome the domain bias of this relaxation scheme we propose a symmetric successive relaxation model. This is demonstrated through a Chebyshev acceleration technique. We conclude by stating that iterative solvers are more superior and consistent techniques for portfolio optimization.
Keywords
Iterative Solvers, Portfolio Optimization, Successive Over Relaxation, Chebyshev Accelaration, Jacobi And Gauss-seidel Algorithms
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- A. Kreinin, Merkoulovitch, L., Rosen, D., and Z. Michael (1998), “Measuring Portfolio Risk Using Quasi Monte Carlo Methods”, ALGO Research Quarterly, 117-25
- A. Lucas, and P. Klaassen (1998), “Extreme Returns, Downside Risk, and Optimal Asset Allocation”, Journal of Portfolio Management, 25,71-79.
- D. Duffie and J. Pan(1997), “An Overview of Value-at-Risk”, Journal of Derivatives, 4, 7-49.
- F. Stambaugh (1996), “Risk and Value-at-Risk”, European Management Journal, 14, 612-621.
- H. Konno and H. Yamazaki (1991), “Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market”, Management Science, 37, 519-531.
- H.M. Markowitz (1952), “Portfolio Selection”, Journal of Finance, 7, 77-91.
- Mausser, H. and D. Rosen (1991), “Beyond VaR: From Measuring Risk to Managing Risk”, ALGO Research Quarterly, 5-20.
- K. Simons (1996), “Value-at-Risk New Approaches to Risk Management”, New England Economic Review, 3-13.
- M. Pritsker (1997), “Evaluating Value at Risk Methodologies”, Journal of Financial Services Research, , 201-242.
- M.R. Young (1998), “A Minimax Portfolio Selection Rule with Linear Programming Solution”, Management Science, 445, 673-683.
- N. Bucay and D. Rosen (1999), “Credit Risk of an International Bond Portfolio: a Case Study”, ALGO Research Quarterly, 29-29.
- P. Artzner, Delbaen F., Eber, J.M., and D. Heath (1997), “Thinking Coherently”, Risk, 10, 68-71.
- P. Embrechts (1999), “Extreme Value Theory as a Risk Management Tool”, North American Actuarial Journal, 3.
- P. Artzner, Delbaen F., Eber, J.M., and D. Heath (1999), “Coherent Measures of Risk”, Mathematical Finance, 9, 203-228.
- Dembo, R.S. and D. Rosen (1999), “The Practice of Portfolio Replication: A Practical Overview of Forward and Inverse Problems”, Annals of Operations Research, 85, 267-284.
- R.T. Rockafellar and S. Uryasev (2000), “Optimization of Conditional Value-at-Risk”, The Journal of Risk,
- R. Litterman (1997), “Hot Spots and Hedges”, Risk, 10, 42-45.
- S. Uryasev (2000), “Conditional Value-at-Risk”, Optimization Algorithms and Applications Financial Engineering News, 14.
- T. Stublo Beder (1995), “VAR: Seductive but Dangerous”, Financial Analysts Journal, 12-24.
- W.T. Ziembaand and J.M. Mulvey (1998), “Worldwide Asset and Liability Modeling”, Cambridge University Press.
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