Optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints

Yuan, Haili; Hu, Yijun

doi:10.1016/j.insmatheco.2009.08.012

Cited by 9 publications

(8 citation statements)

References 11 publications

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“…We will give (rough) sketch of the derivation. From the agent's wealth dynamics in (6), we obtain the budget constraint…”

Section: The Optimization Problemmentioning

confidence: 99%

“…They have studied the portfolio selection problem with a general utility function and a downside consumption constraint using the martingale approach. Yuan and Hu [6] have investigated the optimal consumption and portfolio selection problem with a consumption habit constraint and a terminal wealth downside constraint using the martingale approach. In this paper we use the dynamic programming method based on Karatzas et al [7] to derive the value function and the optimal policies in closed-form with a constant absolute risk aversion (CARA) utility function and a subsistence consumption constraint.…”

Section: Introductionmentioning

confidence: 99%

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Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

Shim¹,

Shin

2014

Mathematical Problems in Engineering

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We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

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“…We will give (rough) sketch of the derivation. From the agent's wealth dynamics in (6), we obtain the budget constraint…”

Section: The Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

Shim¹,

Shin

2014

Mathematical Problems in Engineering

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“…A subsistence consumption constraint means that there is a positive minimum level for consumption such that the agent can live with. Lakner and Nygren [14] and Yuan and Hu [23] considered the optimal consumption and portfolio selection with both consumption and terminal wealth downside constraints on a finite time horizon. For an infinite time horizon case, Gong and Li [8], Shin et al [21] and Shim and Shin [20] investigated the portfolio selection problem using the dynamic programming method or the martingale method.…”

Section: Introductionmentioning

confidence: 99%

Finite time-horizon optimal investment and consumption with time-varying subsistence consumption constraints

Jeon

Kang

Shin

2020

Japan J. Indust. Appl. Math.

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In this paper we consider a general optimal consumption and portfolio selection problem of a finitely-lived agent whose consumption rate process is subject to timevarying subsistence consumption constraints. That is, her consumption rate should be greater than or equal to some convex, non-decreasing and continuous function of time t. Using martingale duality approach and Feynman-Kac formula, we derive the partial differential equation of the Cauchy problem satisfied by the dual value function. We use the integral transform method for solving this Cauchy problem to obtain the general optimal policies in an explicit form. With constant relative risk aversion and constant absolute risk aversion utility functions we illustrate some numerical results of the optimal policies.

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“…The existence of a subsistence consumption constraint has a significant impact on the agent's optimal consumption and investment policies, especially when the constraints are binding. Cox and Huang [2], Gong and Li [4], Huang and Pagès [6], Koo et al [8], Lakner and Nygren [9], Lee and Shin [10], Lim et al [11], Shim and Shin [15], Shin and Lim [16], Shin et al [17], and Yuan and Hu [18] have studied optimal consumption and portfolio selection problems with subsistence consumption constraints.…”

Section: Introductionmentioning

confidence: 99%