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 |
|---|---|
| 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
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Portfolio optimization under the stochastic elasticity of variance. / Yang, Sung Jin; Lee, Min Ku; Kim, Jeong Hoon.
In: Stochastics and Dynamics, Vol. 14, No. 3, 1350024, 09.2014.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 -