An Explicit Solution for Optimal Investment in Heston Model

Boguslavskaya, Elena; Muravey, Dmitry

doi:10.1137/s0040585x97t987946

Cited by 10 publications

(2 citation statements)

References 7 publications

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“…It is obvious to see that the assumed solution expression depends on the form of the utility function. For example, Bian and Zheng, 13 Boguslavskaya and Muravey, 14 Bäuerle and Desmettre 5 give explicit forms of the solution for the power utility maximization problem. However, in other more general forms of utility functions, the expression of the solution for the HJB equation is often difficult to be determined and in fact, the existence of the solution also remains to be unknown, especially for some multivariate models.…”

Section: Introductionmentioning

confidence: 99%

Transition density function expansion methods for portfolio optimization

Lu,

Zhou,

et al. 2024

Optim Control Appl Methods

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In this study, we introduce transition density function expansion methods inspired from Yang et al. (J Econom. 2019;209(2):256–288.) to stochastic control issues related to utility maximization, without imposing limitations on the variety of asset price models and utility functions. Utilizing Bellman's dynamic programming principle, we initially recast the conditional expectation via the transition density function pertinent to the diffusion process. Subsequently, we employ the Itô‐Taylor expansion and Delta expansion techniques to the transition density function associated with the multivariate diffusion process, facilitated by a quasi‐Lamperti transformation, aiming to derive explicit recursive expressions for expansion coefficient functions. Our main contributions are that we articulate detailed algorithms, stemming from the backward recursive formulations of the value function and optimal strategies, achieved through discretization methodologies with rigorous proof of expansion convergence in portfolio optimization. Both theoretical and practical demonstrations are presented to validate the convergence of these approximate techniques in addressing stochastic control challenges. To underscore the efficiency and precision of our proposed methods, we apply them to portfolio selection problems within several benchmark models, and highlight the reduced complexity in comparison to the current methodologies.

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Section: Introductionmentioning

confidence: 99%

Transition density function expansion methods for portfolio optimization

Lu,

Zhou,

et al. 2024

Optim Control Appl Methods

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“…To overcome this limitation, in 1993, Heston suggested Heston's stochastic volatility (HSV) model [6]. The HSV model has been extended in finance for modeling the dynamics of implied volatilities and providing their user with simple breakeven accounting conditions for the profit and loss (S&P) of a hedged position [2,[7][8][9][10][11][12][13][14][15][16][17]].…”

Section: Introductionmentioning

confidence: 99%

Computational technique for simulating variable-order fractional Heston model with application in US stock market

2018

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In this paper, a numerical technique is developed to discretize variable-order fractional Heston differential equation. The proposed strategy is followed by an optimization technology, genetic algorithm, for tuning the unknown parameters in the proposed model. The performance of the model is analyzed to profit and loss 500 close index from the US stock markets. Simulations illustrate the application of the proposed technique.

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Robust Optimal Investment Problem with Delay under Heston’s Model

Zhao

2021

Methodol Comput Appl Probab

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This paper considers a robust optimal portfolio problem under Heston model in which the risky asset price is related to the historical performance. The finance market includes a riskless asset and a risky asset whose price is controlled by a stochastic delay equation. The objective is to choose the investment strategy to maximize the minimal expected utility of terminal wealth. By employing dynamic programming principle and Hamilton-Jacobin-Bellman (HJB) equation, we obtain the specific expression of the optimal control and the explicit solution of the corresponding HJB equation. Besides, a verification theorem is provided to ensure the value function is indeed the solution of the HJB equation. Finally, we use numerical examples to illustrate the relationship between the optimal strategy and parameters.

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An Explicit Solution for Optimal Investment in Heston Model

Cited by 10 publications

References 7 publications

Transition density function expansion methods for portfolio optimization

Transition density function expansion methods for portfolio optimization

Computational technique for simulating variable-order fractional Heston model with application in US stock market

Robust Optimal Investment Problem with Delay under Heston’s Model

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