Numerical Solutions to Dynamic Portfolio Problems: The Case for Value Function Iteration using Taylor Approximation

Garlappi, Lorenzo; Skoulakis, Georgios

doi:10.1007/s10614-008-9156-0

Cited by 24 publications

(28 citation statements)

References 18 publications

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“…In fact, these authors provided evidence that there should exist minor discrepancies between results under discrete and continuous time models. Thus, numerical results that we derive from continuous time are indirectly comparable to those of Garlappi and Skoulakis (2009). We show that, for large degrees of risk aversion and/or small horizon, when the state variable closes to its unconditional mean, the two numerical results are quite similar.…”

Section: Introductionsupporting

confidence: 62%

“…We show that, for large degrees of risk aversion and/or small horizon, when the state variable closes to its unconditional mean, the two numerical results are quite similar. Otherwise, results under our explicit solution in continuous time exhibit some discrepancies with Garlappi and Skoulakis (2009) when the risk aversion decreases and/or when the time horizon increases. We argue that this is due to large sensitivity of total demand to state variable (Sharpe ratio).…”

Section: Introductionmentioning

confidence: 68%

See 1 more Smart Citation

Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

Legendre

Togola²

2016

Economic Modelling

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This paper solves the dynamic portfolio choice problem. Using an explicit solution with a power utility, we construct a bridge between a continuous and discrete VAR model to assess portfolio sensitivities. We find, from a well analyzed example that the optimal allocation to stocks is particularly sensitive to Sharpe ratio. Our quantitative analysis highlights that this sensitivity increases when the risk aversion decreases and/or when the time horizon increases. This finding explains the low accuracy of discrete numerical methods especially along the tails of the unconditional distribution of the state variable.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 68%

Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

Legendre

Togola²

2016

Economic Modelling

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“…We first study a CRRA utility optimization example. It has been noted that a simulationand-regression approach can generate large numerical errors when the utility function is highly nonlinear (high risk aversion), see for example Van Binsbergen and Brandt (2007), Garlappi andSkoulakis (2009) andDenault andSimonato (2017). We apply the two-stage LSMC method and the classical LSMC method to CRRA utility optimization, and then compare the resulting initial value function estimatesv 0 = 1 M M m=1 (Ŵ t N ) 1−γ /(1−γ) for a one-year time horizon with monthly rebalancing.…”

Section: Model Validationmentioning

confidence: 99%

Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method

Zhang

Langrené²,

Tian³

et al. 2019

JCF

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In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of return, as it simultaneously seeks a desired expected return, cuts off downside risk, and implicitly caps volatility and higher moments. To illustrate the effectiveness of this investment strategy, we study a multi-period portfolio optimization problem with transaction costs, and develop a two-stage regression approach that improves the classical least squares Monte Carlo algorithm when dealing with difficult payoffs such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical least squares Monte Carlo algorithm for both the constant relative risk aversion (CRRA) utility approach and the proposed skewed target range strategy (STRS). Our numerical results illustrate the ability of the STRS to contain the portfolio value within the targeted range. Compared to the CRRA utility approach, the STRS achieves a similar mean-variance efficient frontier while delivering a better downside risk-return trade-off.

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“…We consider the vector auto-regression (VAR) model to describe the dynamics of the log excess return r e t of the risky asset and its log dividend yield d t , that are chosen as the state variables. Quarterly data are generated with the following process, as in Brandt et al (2005), van Binsbergen and Brandt (2007b) and Garlappi and Skoulakis (2009) In most of the tests, the initial state, d 0 , is chosen as the unconditional mean, i.e., d 0 = −0.155/(1 − 0.958) = −3.6905. Only in Sect.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…They state that the vBB algorithm is more stable than the BGSS algorithm, since the BGSS algorithm essentially relies on an approximation of the utility function. Many other numerical approaches for computing conditional expectations have been considered, for example, in Barberis (2000), Jondeau and Rockinger (2006) and Garlappi and Skoulakis (2009).…”

Section: Introductionmentioning

confidence: 99%

Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem

Cong

Oosterlee

2015

SSRN Journal

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This paper enhances a well-known dynamic portfolio management algorithm, the BGSS algorithm, proposed by Brandt et al. (Review of Financial Studies, 18(3):831-873, 2005). We equip this algorithm with the components from a recently developed method, the Stochastic Grid Bundling Method (SGBM), for calculating conditional expectations. When solving the first-order conditions for a portfolio optimum, we implement a Taylor series expansion based on a nonlinear decomposition to approximate the utility functions. In the numerical tests, we show that our algorithm is accurate and robust in approximating the optimal investment strategies, which are generated by a new benchmark approach based on the COS method (Fang and Oosterlee, in SIAM Journal of Scientific Computing, 31(2): 2008).

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Numerical Solutions to Dynamic Portfolio Problems: The Case for Value Function Iteration using Taylor Approximation

Abstract: Portfolio choice, Numerical solution, Value function iteration,

Cited by 24 publications

References 18 publications

Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method

Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem

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