Journal ArticleDOI
Resolution of Degeneracy in Merton's Portfolio Problem
Chi Seng Pun,Hoi Ying Wong +1 more
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TLDR
This study proposes a constrained $\ell_1$-minimization approach to resolve the degeneracy in the high-dimensionalSetting and stabilize the performance in the low-dimensional setting and proves the consistency of the framework that the estimate of the optimal control tends to be the optimal value.Abstract:
The Merton problem determines the optimal intertemporal portfolio choice by maximizing the expected utility, and is the basis of modern portfolio theory in continuous-time finance. However, its empirical performance is disappointing. The estimation errors of the expected rates of returns make the optimal policy degenerate, resulting in an extremely low (or unbounded) expected utility value for a high-dimensional portfolio. We further prove that the estimation error of the variance-covariance matrix leads to the degenerated policy of solely investing in the risk-free asset. This study proposes a constrained l1 - minimization approach to resolve the degeneracy. The proposed scheme can be implemented with simple linear programming and involves negligible additional computational time, compared to standard estimation. We prove the consistency of our framework that our estimate of the optimal control tends to be the true one. We also derive the rate of convergence. Simulation studies are provided to verify the finite-sample properties. An empirical study using S&P 500 component stock data demonstrates the superiority of the proposed approach.read more
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References
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Journal ArticleDOI
The Dantzig selector: Statistical estimation when p is much larger than n
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In many important statistical applications, the number of variables or parameters p is much larger than the total number of observations n as discussed by the authors, and it is possible to estimate β reliably based on the noisy data y.
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Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?
TL;DR: In this article, the authors evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio.
Book ChapterDOI
Estimation with Quadratic Loss
W. James,Charles Stein +1 more
TL;DR: In this paper, the authors consider the problem of finding the best unbiased estimator of a linear function of the mean of a set of observed random variables. And they show that for large samples the maximum likelihood estimator approximately minimizes the mean squared error when compared with other reasonable estimators.
Book
Continuous-Time Finance
TL;DR: In this article, the authors introduce the concept of Continuous-Time Models and propose a model for portfolio selection and portfolio selection in a continuous-time model, based on the theory of rational option pricing and the Modigliani-Miller Theorem.
Journal ArticleDOI
The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice
TL;DR: The basic theory and extensions of mean-variance analysis are discussed in Markowitz as discussed by the authors and Ziemba & Vickson [1975] and Bawa, Brown & Klein [1979] and Michaud [1989] review some of its problems.
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A linear programming model for selection of sparse high-dimensional multiperiod portfolios
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