Optimal portfolio and consumption with habit formation in a jump diffusion market

Ruan, Xinfeng; Zhu, Wei; Hu, Jin; Huang, Jiexiang

doi:10.1016/j.amc.2013.07.063

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…Li et al [8] studied the threshold dividend strategy for renewal jump-diffusion process. Ruan et al [9] studied the optimal portfolio and consumption with habit formation in a jump-diffusion market.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

Sheng

Rong

Zhao

2014

Abstract and Applied Analysis

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This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motionsW(t)andW1(t). A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealthxand decreasing with the volatility rate of risk asset price. However, the optimal value functionV(t;x;s)is increasing with the appreciation rateμof risk asset.

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Section: Introductionmentioning

confidence: 99%

Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

Sheng

Rong

Zhao

2014

Abstract and Applied Analysis

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“…To tackle jumps in stock price, Merton [24] extended the GBM model to a jump-diffusion model for option pricing. Under this model, Aase [1] studied the optimal portfolio-consumption problem on a finite-time horizon; Framstad et al [10] considered the problem on an infinite-time horizon in the presence of proportional transaction costs with constant relative risk aversion utility; Ruan et al [27] investigated the optimal problem with habit formulation in an incomplete market using the maximum principle; Guambe and Kufakunesu [14] extended the work of Shen and Wei [29] to a geometric Itô-Lévy jump process [7], and solved the problem by combining the Hamilton-Jacobi-Bellman (HJB) equation [32] and a backward stochastic differential equation (SDE); Nguyen [25] examined the problem with downside risk constraint. Apart from the diffusion and jump-diffusion models, there are some other models to describe financial markets in the literature.…”

Section: Introductionmentioning

confidence: 99%

Optimal Portfolio and Consumption for a Markovian Regime-Switching Jump-Diffusion Process

Zhang¹,

Liang²,

Yuen³

2021

ANZIAM J.

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We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

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Errata corrige optimal portfolio and consumption with habit formation in a jump diffusion market

Ruan

Zhu

et al. 2014

Applied Mathematics and Computation

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Optimal portfolio and consumption with habit formation in a jump diffusion market

Cited by 5 publications

References 24 publications

Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

Optimal Portfolio and Consumption for a Markovian Regime-Switching Jump-Diffusion Process

Errata corrige optimal portfolio and consumption with habit formation in a jump diffusion market

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