Multi-period stochastic optimization models for dynamic asset allocation

Hibiki, Norio

doi:10.1016/j.jbankfin.2005.04.027

Cited by 49 publications

(34 citation statements)

References 8 publications

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“…We have generated scenarios of total return, R s i,t , in a simple manner similar to [8]. We have first collected historical data of asset price from the Yahoo finance Japan.…”

Section: Scenario Generationmentioning

confidence: 99%

A polynomial optimization approach to constant rebalanced portfolio selection

Takano

Sotirov

2011

Comput Optim Appl

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We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.

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“…We have generated scenarios of total return, R s i,t , in a simple manner similar to [8]. We have first collected historical data of asset price from the Yahoo finance Japan.…”

Section: Scenario Generationmentioning

confidence: 99%

A polynomial optimization approach to constant rebalanced portfolio selection

Takano

Sotirov

2011

Comput Optim Appl

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“…Hibiki (2006) proposed an iterative optimization algorithm by alternately fixing decision variables for approximately solving the hybrid model with a fixed-proportion strategy. In this strategy, investment proportions have the same value for all simulated paths passing the same bundle of states.…”

Section: [ Validity As An Investmentmentioning

confidence: 99%

“…Although this algorithm works well by employing a good initial solution, it may not work in the constant rebalanced portfolio optimization in question because initial solution can be hardly improved due to the excessive reduction of degree of freedom. Besides, transaction costs are not considered in Hibiki (2006). Transaction Costs.…”

Section: [ Validity As An Investmentmentioning

confidence: 99%

“…In contrast to the use of nonlinear programming solver, the proposed strategy can provide a solution to the complex problem. Moreover, an incumbent solution can be improved better than the alternating optimization (Hibiki, 2006).…”

Section: [ Validity As An Investmentmentioning

confidence: 99%

“…However, seeking accuracy in the uncertainty representation, the size of the optimization problem may grow exponentially (Ermoliev and Wets, 1988). On the other hand, simulated path model, in which scenarios are represented by sample paths generated by a Monte Carlo simulation method, yields better accuracy in describing uncertainty (Hibiki, 2003). Incorporating the benefits of the two approaches, Hibiki (2003) proposed a hybrid (bundling simulated path) model which is designed not only to describe uncertainty on a simulated path structure but also to enable one to make conditional decisions in a tree structure.…”

Section: Introductionmentioning

confidence: 99%

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Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

Takano

Gotoh

2010

Asia-Pac Financ Markets

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In this paper, we study a multi-period portfolio optimization where conditional value-atrisk (CVaR) is controlled as well as expected return, and the so-called constant rebalancing strategy is employed under nonlinear transaction costs. In general, the optimization of this strategy itself is, however, difficult to attain a globally optimal solution because of the nonconvexity. In addition, nonlinearity of the transaction cost and CVaR functions makes things worse, and even a locally optimal solution may not be reached via a state-of-the-art nonlinear programming solver when the size of the problem is large. In order to provide a practical solution to the highly complex problem, we propose a local search algorithm where linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the proposed algorithm attains a good solution in practical time even when a revised version of an existing global optimization approach cannot return any feasible solutions.

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Knowledge‐based scenario tree generation methods and application in multiperiod portfolio selection problem

Chen

2013

Appl Stoch Models Bus & Ind

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A scenario tree is an efficient way to represent a stochastic data process in decision problems under uncertainty. This paper addresses how to efficiently generate appropriate scenario trees. A knowledge‐based scenario tree generation method is proposed; the new method is further improved by accounting for subjective judgements or expectations about the random future. Compared with existing approaches, complicated mathematical models and time‐consuming estimation, simulation and optimization problem solution are avoided in our knowledge‐based algorithms, and large‐scale scenario trees can be quickly generated. To show the advantages of the new algorithms, a multiperiod portfolio selection problem is considered, and a dynamic risk measure is adopted to control the intermediate risk, which is superior to the single‐period risk measure used in the existing literature. A series of numerical experiments are carried out by using real trading data from the Shanghai stock market. The results show that the scenarios generated by our algorithms can properly represent the underlying distribution; our algorithms have high performance, say, a scenario tree with up to 10,000 scenarios can be generated in less than a half minute. The applications in the multiperiod portfolio management problem demonstrate that our scenario tree generation methods are stable, and the optimal trading strategies obtained with the generated scenario tree are reasonable, efficient and robust. Copyright © 2013 John Wiley & Sons, Ltd.

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Multi-period stochastic optimization models for dynamic asset allocation

Cited by 49 publications

References 8 publications

A polynomial optimization approach to constant rebalanced portfolio selection

A polynomial optimization approach to constant rebalanced portfolio selection

Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

Knowledge‐based scenario tree generation methods and application in multiperiod portfolio selection problem

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