Enhanced group analysis of a semi linear generalization of a general bond-pricing equation

Bozhkov, Yuri; Dimas, S.

doi:10.1016/j.cnsns.2017.06.006

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…However,g(s, t) is independent of v and cp = 0; therefore, there is no solution for this transformed equation (20) with the terminal conditiong(s, T ) = 1. This is unexpected.…”

Section: Symmetry Analysis Of (10) and The First Similarity Reductionmentioning

confidence: 99%

“…Khalique et al solved the optimal investment-consumption problem under the constant elasticity of variance (CEV) model using the invariant approach [18]. Furthermore, the complete and enhanced group classifications of generalization of the Black-Scholes-Merton model and a semi-linear generalization of a general bond-pricing equation were carried out from the mathematical point by making use of the underlying equivalence and additional equivalence transformations [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility

2021

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In this article, explicit representation of solution for the Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem for an investor who seeks to maximize the expected power (CRRA) utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model is derived based on the application of the Lie symmetry method to the partial differential equation and its associated terminal condition. Compared with the ingenious ansatz techniques used before, here we present a group theoretical analysis of the terminal value problem for the solution following the algorithmic procedure of the Lie symmetry analysis. It shows that the interesting properties of the group structures of the original HJB equation and its successive similarity reduced equations lead to an elegant resolution of the problem. Moreover, we identify the meaningful range of risk aversion coefficient which is ignored in the previous work. At last, the properties and sensitivity analysis of the derived optimal strategy are demonstrated by numerical simulations and several figures. The method used here is quite general and

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“…However,g(s, t) is independent of v and cp = 0; therefore, there is no solution for this transformed equation (20) with the terminal conditiong(s, T ) = 1. This is unexpected.…”

Section: Symmetry Analysis Of (10) and The First Similarity Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility

2021

View full text Add to dashboard Cite

show abstract

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

2020

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Enhanced group analysis of a semi linear generalization of a general bond-pricing equation

Cited by 2 publications

References 24 publications

Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility

Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

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