Family optimal investment strategy for a random household expenditure under the CEV model

Yuan, Weipeng; Lai, Shaoyong

doi:10.1016/j.cam.2019.01.001

Cited by 25 publications

(6 citation statements)

References 22 publications

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“…Hipp and Plum [1], David Promislow and Young [2], Milevsky et al [3], Chen et al [4], and Bayraktar and Zhang [5] consider the optimal investment for minimizing the ruin probability. Wang [6], Bo and Capponi [7], Delong [8], Yuan and Lai [9], and Li et al [10] obtain the optimal investment strategy under maximizing the expected utility of terminal wealth.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to Yuan and Lai [9] and Li et al [10], we study households with stochastic expenditure optimal investment strategies. Unlike them, we consider that households can invest in corporate bonds and study the optimal timeconsistent strategy under the mean-variance.…”

Section: Introductionmentioning

confidence: 99%

“…Remark 1 (i) From eorem 2, we can find that the amounts invested in risky assets p * i and 􏽥 p * i are influenced by the diffusion parameter β of random expenditures but are independent of the drift parameter α of random expenditures. is is the same as Yuan and Lai [9]. By equations (B.…”

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confidence: 99%

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Optimal Time‐Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance

Guan¹,

Yuan²,

2021

Complexity

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Considering the mind of rivalry between families, each family focuses not only on its own wealth but also on other families, especially neighbors. In this paper, we investigate the non-zero-sum mean-variance game between two families with a random household expenditure under the default risk and relative performance. Applying the stochastic control theory within the framework of the game theory, the extended Hamilton–Jacobi–Bellman equation equations are derived. By solving this equation, we obtain the Nash equilibrium strategies of the two families and the corresponding equilibrium value functions. We also provide a numerical example to analyze the effects of relevant parameters on Nash equilibrium strategy and on the utility loss due to the mind of rivalry.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Time‐Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance

Guan¹,

Yuan²,

2021

Complexity

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“…Specifically, the Legendre dual transformation technique introduced by Xiao et al [16] and then heavily used in many of the aforementioned works (see Gao [17,18] and Jung and Kim [19]) to reduce the HJB equation into a linear pde cannot be directly adapted to models with general correlation. For example, following the way, Wang et al [26] and Yuan and Lai [33] assumed that the correlation equals to ± 1 to remove the nonlinear parts of the HJB equation. In this paper, instead of that method, we directly conjecture the functional form of the value function and by which the HJB equation can be directly simplified into two parabolic pdes.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

Liu

2020

Mathematical Problems in Engineering

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This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

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“…See Refs. [45][46][47] for recent and successfully applications of the CEV model in different contexts.…”

Section: Introductionmentioning

confidence: 99%

The fractional and mixed-fractional CEV model

Araneda

2020

Journal of Computational and Applied Mathematics

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The continuous observation of the financial markets has identified some 'stylized facts' which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the long-range dependence has been faced replacing the traditional Gauss-Wiener process (Brownian motion), characterized by stationary independent increments, by a fractional version. On the other hand, the CEV model addresses the Leverage effect and smile-skew phenomena, efficiently. In this paper, these two insights are merging and both the fractional and mixed-fractional extensions for the CEV model, are developed. Using the fractional versions of both the Itô's calculus and the Fokker-Planck equation, the transition probability density function of the asset price is obtained as the solution of a non-stationary Feller process with time-varying coefficients, getting an analytical valuation formula for a European Call option. Besides, the Greeks are computed and compared with the standard case.

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Family optimal investment strategy for a random household expenditure under the CEV model

Cited by 25 publications

References 22 publications

Optimal Time‐Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance

Optimal Time‐Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance

Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

The fractional and mixed-fractional CEV model

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