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Volume 31, Issue 3
A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model

Yingli Hou & Guoxin Liu

DOI: 10.13447/j.1674-5647.2015.03.06

Commun. Math. Res., 31 (2015), pp. 242-252.

Published online: 2021-05

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  • Abstract

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment (no-shorting). First, a Lagrange multiplier is introduced to simplify the mean-variance problem and the corresponding Hamilton-Jacobi-Bellman (HJB) equation is established. Via a power transformation technique and variable change method, the optimal strategies with the Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem, the optimal strategies and optimal value for the original problem (i.e., the efficient strategies and efficient frontier) are derived explicitly.

  • Keywords

constant elasticity of variance model, mean-variance, optimal strategy.

  • AMS Subject Headings

49J20, 60J60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-242, author = {Hou , Yingli and Liu , Guoxin}, title = {A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {3}, pages = {242--252}, abstract = {

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment (no-shorting). First, a Lagrange multiplier is introduced to simplify the mean-variance problem and the corresponding Hamilton-Jacobi-Bellman (HJB) equation is established. Via a power transformation technique and variable change method, the optimal strategies with the Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem, the optimal strategies and optimal value for the original problem (i.e., the efficient strategies and efficient frontier) are derived explicitly.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.03.06}, url = {http://global-sci.org/intro/article_detail/cmr/18926.html} }
TY - JOUR T1 - A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model AU - Hou , Yingli AU - Liu , Guoxin JO - Communications in Mathematical Research VL - 3 SP - 242 EP - 252 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.03.06 UR - https://global-sci.org/intro/article_detail/cmr/18926.html KW - constant elasticity of variance model, mean-variance, optimal strategy. AB -

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment (no-shorting). First, a Lagrange multiplier is introduced to simplify the mean-variance problem and the corresponding Hamilton-Jacobi-Bellman (HJB) equation is established. Via a power transformation technique and variable change method, the optimal strategies with the Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem, the optimal strategies and optimal value for the original problem (i.e., the efficient strategies and efficient frontier) are derived explicitly.

Hou , Yingli and Liu , Guoxin. (2021). A Mean-Variance Problem in the Constant Elasticity of Variance (CEV) Model. Communications in Mathematical Research . 31 (3). 242-252. doi:10.13447/j.1674-5647.2015.03.06
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