### Abstract

Based on the observation that the elasticity of variance of risky assets is randomly varying around a constant, we take an underlying asset model in which the averaged constant elasticity of variance is perturbed by a small fast fluctuating process and study the Merton type portfolio optimization problem using dynamic programming as well as asymptotic expansions. The Hamilton-Jacobi-Bellman equation for each of the power and exponential utility functions leads to an optimal trading strategy as a perturbation around the well known one. We reveal the impact of both the constant elasticity of variance upon the Merton investment optimal control under the Black-Scholes model and the stochastic elasticity of variance upon the investment optimal control under the constant elasticity of variance model. The concavity of the investment policy with respect to the excess return is characteristic of a market economy with the constant or stochastic elasticity of variance.

Original language | English |
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Article number | 1350024 |

Journal | Stochastics and Dynamics |

Volume | 14 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 Sep |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation

### Cite this

*Stochastics and Dynamics*,

*14*(3), [1350024]. https://doi.org/10.1142/S021949371350024X

}

*Stochastics and Dynamics*, vol. 14, no. 3, 1350024. https://doi.org/10.1142/S021949371350024X

**Portfolio optimization under the stochastic elasticity of variance.** / Yang, Sung Jin; Lee, Min Ku; Kim, Jeong Hoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Portfolio optimization under the stochastic elasticity of variance

AU - Yang, Sung Jin

AU - Lee, Min Ku

AU - Kim, Jeong Hoon

PY - 2014/9

Y1 - 2014/9

N2 - Based on the observation that the elasticity of variance of risky assets is randomly varying around a constant, we take an underlying asset model in which the averaged constant elasticity of variance is perturbed by a small fast fluctuating process and study the Merton type portfolio optimization problem using dynamic programming as well as asymptotic expansions. The Hamilton-Jacobi-Bellman equation for each of the power and exponential utility functions leads to an optimal trading strategy as a perturbation around the well known one. We reveal the impact of both the constant elasticity of variance upon the Merton investment optimal control under the Black-Scholes model and the stochastic elasticity of variance upon the investment optimal control under the constant elasticity of variance model. The concavity of the investment policy with respect to the excess return is characteristic of a market economy with the constant or stochastic elasticity of variance.

AB - Based on the observation that the elasticity of variance of risky assets is randomly varying around a constant, we take an underlying asset model in which the averaged constant elasticity of variance is perturbed by a small fast fluctuating process and study the Merton type portfolio optimization problem using dynamic programming as well as asymptotic expansions. The Hamilton-Jacobi-Bellman equation for each of the power and exponential utility functions leads to an optimal trading strategy as a perturbation around the well known one. We reveal the impact of both the constant elasticity of variance upon the Merton investment optimal control under the Black-Scholes model and the stochastic elasticity of variance upon the investment optimal control under the constant elasticity of variance model. The concavity of the investment policy with respect to the excess return is characteristic of a market economy with the constant or stochastic elasticity of variance.

UR - http://www.scopus.com/inward/record.url?scp=84901839364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901839364&partnerID=8YFLogxK

U2 - 10.1142/S021949371350024X

DO - 10.1142/S021949371350024X

M3 - Article

AN - SCOPUS:84901839364

VL - 14

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

SN - 0219-4937

IS - 3

M1 - 1350024

ER -