Multi-Period Stochastic Programming Models for Dynamic Asset Allocation

Hibiki, Norio

doi:10.5687/sss.2000.37

Cited by 4 publications

(8 citation statements)

References 7 publications

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“…Path grouping By analogy with the standard non-anticipativity constraints (10) for scenario trees, one may require identical decisions to be made on scenarios that possess similar properties at a given time t. This leads to the idea of path grouping, also known as "path bundling" (see similar approaches in Titley, 1993;Hibiki, 1999Hibiki, , 2001Bogentoft, Romeijn, and Uryasev 2001). At each time t, the J sample paths in the collection S are partitioned…”

Section: Modeling the Market Impactmentioning

confidence: 99%

“…For the most part, this approach has been employed in the area of pricing of derivatives (Titley, 1993, Boyle, Broadie, andBroadie and Glasserman, 1997;Carriere, 1996;Barraquand and Martineau, 1995;etc.). Recently, the sample-path framework was applied to solving dynamic asset and liability management problems (Bogentoft, Romeijn, and Uryasev 2001;Hibiki, 1999Hibiki, , 2001. In the present paper we consider the concept of sample-path scenario sets and corresponding optimization techniques in application to a problem of optimal transaction execution in presence of market imperfections and friction.…”

Section: General Definitions and Problem Statementmentioning

confidence: 99%

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A sample-path approach to optimal position liquidation

Krokhmal

Uryasev

2006

Ann Oper Res

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We consider the problem of optimal position liquidation where the expected cash flow stream due to transactions is maximized in the presence of temporary or permanent market impact. A stochastic programming approach is used to construct trading strategies that differentiate decisions with respect to the observed market conditions, and can accommodate various types of trading constraints. As a scenario model, we use a collection of sample paths representing possible future realizations of state variable processes (price, trading volume etc.), and employ a heuristical technique of sample-path grouping, which can be viewed as a generalization of the standard nonanticipativity constraints.

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Section: Modeling the Market Impactmentioning

confidence: 99%

Section: General Definitions and Problem Statementmentioning

confidence: 99%

A sample-path approach to optimal position liquidation

Krokhmal

Uryasev

2006

Ann Oper Res

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“…The hybrid model allows conditional decisions to be made for similar states bundled at each time using sample returns generated by the Monte Carlo method [6,8,9]. We can use a tree or lattice structure to make conditional decisions.…”

Section: Modeling Using State-dependent Function With Cvar 21 Hybrimentioning

confidence: 99%

“…We can use a tree or lattice structure to make conditional decisions. 6 A rule that the same investment decisions are made in similar states is defined to satisfy the non-anticipativity. Hybrid N4 model Hybrid N1 model We employ the lattice structure as the modeling structure with respect to the decision nodes in this paper.…”

Section: Modeling Using State-dependent Function With Cvar 21 Hybrimentioning

confidence: 99%

“…A return distribution is described using simulated paths generated by the Monte Carlo method. Hibiki [6,8,9] develop a hybrid model involving conditional decisions in the simulated path approach. 3 In the hybrid model, similar states are bundled at each time so that the same conditional decisions can be made, though the decisions are not strictly state-dependent.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Period Stochastic Programming Model for State-Dependent Asset Allocation With Cvar

Hirano¹,

Hibiki

2015

JORSJ

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We need to solve a multi-period optimization problem to decide dynamic investment policies under various practical constraints. Hibiki ( ,2003Hibiki ( ,2006) develop a hybrid model where conditional decisions can be made in a simulation approach, and investment proportions are expressed by a step function of the amount of wealth. In this paper, we introduce an idea of a state-dependent function into the hybrid model as well as Takaya and Hibiki (2012). At first, we define the state-dependent function form for a multiple asset allocation problem with CVaR (Conditional Value at Risk) using the hybrid model, and we clarify that the function form is V-shaped and kinked at the VaR point. We propose a piecewise linear model with the V-shaped function to solve the multi-period and state-dependent asset allocation problem. We solve a three-period problem for five assets, and compare the piecewise linear model with the hybrid model. We conduct the sensitivity analysis for different risk averse coefficients and autocorrelations to examine the characteristics of the model. Keywords: finance, stochastic optimization, multi-period asset allocation, simulation IntroductionInstitutional investors need to manage their investment funds in consideration of rebalancing assets during a planning period for efficient asset management. Individual investors who face their long-term financial planning have similar problems. A multi-period optimization model involving dynamic investment decisions explicitly can be used to solve the problem with several constraints in practice. There are many studies in the literatures of different academic fields. In the fields of mathematical finance and financial economics, analytical solutions or approximate solutions are derived employing the HJB equation or the Martingale method under the setting of a continuous time and a continuous distribution. Cvitanić and Karatzas [3] derive a closed form solution of minimizing the first-order lower partial moment (LPM).2 Recently, several Monte Carlo methods have been developed for the computation of optimal portfolio policies (Detemple, Garcia and Rindisbacher [4]). But the number of assets is limited to solve the problem in general, and it is also difficult to derive the optimal solutions for the model with practical constraints. In the fields of financial engineering, the numerical solutions are derived employing mathematical programming under the setting of a discrete time and a discrete distribution in order to solve the multiple assets problem with practical constraints. Hibiki [5] develops a simulated path model to solve the multi-period portfolio optimization problem. A return distribution is described using simulated paths

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Multi-period stochastic optimization models for dynamic asset allocation

Hibiki

2006

Journal of Banking & Finance

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Multi-Period Stochastic Programming Models for Dynamic Asset Allocation

Cited by 4 publications

References 7 publications

A sample-path approach to optimal position liquidation

A sample-path approach to optimal position liquidation

Multi-Period Stochastic Programming Model for State-Dependent Asset Allocation With Cvar

Multi-period stochastic optimization models for dynamic asset allocation

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