Approximate Analytical Solution to Consumption and Long-Term Security Investment Optimization Problem With Homothetic Robust Utility

Batbold, Bolorsuvd; Kikuchi, Kentaro; Kusuda, Koji

doi:10.15807/torsj.62.71

Cited by 8 publications

(19 citation statements)

References 7 publications

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“…where β > 0 is the subjective discount rate, γ > 1 is the relative risk aversion, and ψ > 0 is the elasticity of intertemporal substitution. Batbold et al (2023) introduce the following homothetic robust Epstein-Zin (HREZ) utility.…”

Section: Robust Consumption-investment Problemmentioning

confidence: 99%

“…The sum decomposition shown above is a regularized version of the decomposition shown in Batbold et al (2023).…”

Section: Sum Decompositionmentioning

confidence: 99%

“…In this study, we assume homothetic robust Epstein-Zin utility introduced by Batbold, Kikuchi, and Kusuda (2023) and consider a finite-time consumption-investment problem under the quadratic security market model of Batbold et al (2022). Liu (2010) and Batbold et al (2023) analyze infinite-time consumptioninvestment problems and derive the nonlinear nonhomogeneous partial differential equation (PDE) for the indirect utility function. Because the nonhomogeneous term appearing in the PDE is stable in infinite-time problems, they apply the loglinear approximation method of Campbell and Viceira (2002) to derive an approximate solution.…”

Section: Introductionmentioning

confidence: 99%

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Regularized Robust Strategic Asset Allocation under Stochastic Variance-Covariance of Asset Returns

Kusuda,

Kikuchi

2024

Preprint

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This study considers a finite-time robust consumption-investment problem under a quadratic security market model with stochastic variances and covariances of asset returns, as well as stochastic interest rates, market price of risk, and inflation rates. Because the optimal portfolio is proportional to the inverse of the stochastic variance-covariance matrix of asset returns, it becomes unstable when near-singularity of the variance-covariance matrix occurs. We propose a regularized consumption-investment problem in which the near-singularity risk is introduced into the budget constraint equation as a regularization term. We show that the optimal regularized portfolio can be stable and decomposed into the product of the ''standard deviation,'' ''correlation,'' and ''investment control'' factors. As the optimal regularized robust portfolio contains an unknown function that is a solution to a nonlinear PDE, we derive an approximate optimal regularized portfolio. Our numerical analysis shows that the market timing effects in the approximate optimal regularized asset allocation are significant and nonlinear, and all factors contribute to these market timing effects. JEL classification: C61, G11

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Section: Robust Consumption-investment Problemmentioning

confidence: 99%

“…The sum decomposition shown above is a regularized version of the decomposition shown in Batbold et al (2023).…”

Section: Sum Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Regularized Robust Strategic Asset Allocation under Stochastic Variance-Covariance of Asset Returns

Kusuda,

Kikuchi

2024

Preprint

Self Cite

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“…These optimal consumption-investment decisions implicitly determine the worst-case probability. Homothetic robust utility is used in robust portfolio studies, such as Skiadas (2003), Maenhout (2006), Liu (2010), Branger, Larsen, and Munk (2013), Munk and Rubtsov (2014), Yi, Viens, Law, and Li (2015), Batbold, Kikuchi, and Kusuda (2019), and Kikuchi and Kusuda (2024a) 3 . These studies have done little to elucidate the theoretical structures of the i) budget constraint equation and market price of risk under the conditional worst-case probability and the worst-case probability; and ii) the two types of CAPMs under the base probability and the worst-case probability.…”

Section: Introductionmentioning

confidence: 99%

Robust Control and CAPMs under a Quadratic Security Market Model

Batbold,

Kikuchi,

Kusuda

2024

Preprint

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This study assumes homothetic robust Epstein-Zin utility and analyzes the consumption-investment problem and CAPMs under a quadratic security market model in which interest rates, the market price of risk, the variances and covariances of asset returns, and inflation rates are stochastic. First, we demonstrate that homothetic robust Epstein-Zin utility is interpreted as homothetic stochastic differential utility. Then, we show that robust investors determine the ''worst-case probability'' and the optimal consumption-investment. We clarify the theoretical structures of robust control. We derive a robust version of the two-factor CAPM and show that the CAPM can contribute to solving both the equity premium puzzle and the risk-free rate puzzle. Furthermore, we derive a testable robust ICAPM and demonstrate that the testable ICAPM is consistent with our quadratic security market model. JEL classification C61, D81, G11, G12

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“…4 Homothetic robust utility has been used in various robust control studies including Maenhout [21], Liu [19], Branger, Larsen, and Munk [7], Munk and Rubtsov [22], Yi, Viens, Law, and Li [25], Batbold et al [4], and Kikuchi and Kusuda [16].…”

Section: Introductionmentioning

confidence: 99%

Age-dependent Robust Strategic Asset Allocation with Inflation-Deflation Hedging Demand

Kusuda

Kikuchi

2023

Preprint

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This study analyzes robust strategic asset allocation under a quadratic security market model with stochastic volatility and inflation rates assuming “homothetic age-dependent robust utility” in which relative ambiguity aversion is a decreasing function of age. We consider the finite-time consumption-investment problem and derive a linear approximate optimal robust portfolio decomposed into myopic, intertemporal hedging, and inflation-deflation hedging demands. Our numerical analysis of equity allocations shows modest hump-shaped age effects, similar to the results of a previous empirical analysis, and that the upswing is due to the increase in myopic demand, while the downswing is due to the decline in intertemporal hedging demand. JEL Classification C61 · G11

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Approximate Analytical Solution to Consumption and Long-Term Security Investment Optimization Problem With Homothetic Robust Utility

Cited by 8 publications

References 7 publications

Regularized Robust Strategic Asset Allocation under Stochastic Variance-Covariance of Asset Returns

Regularized Robust Strategic Asset Allocation under Stochastic Variance-Covariance of Asset Returns

Robust Control and CAPMs under a Quadratic Security Market Model

Age-dependent Robust Strategic Asset Allocation with Inflation-Deflation Hedging Demand

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