A utility maximisation problem on multiple time scales

Atıcı, Ferhan M.; Biles, Daniel C.; Lebedinsky, Alex

doi:10.1504/ijdsde.2011.038495

Cited by 3 publications

(11 citation statements)

References 11 publications

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“…, and f(x, y, z, u): R 4 ⟶ R + is a concave in (x, y), continuous, and differentiable real-valued function with f y ≤ 0. e discount factor relating to NSDM (19) is…”

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

“…We mention that the concavity in (x, y) means concavity in two variables x and y jointly, not in each variable separately. e concavity of f(x, y, z, u) is used to find the optimal solution of NSDM (19), namely, function f(x, y, z, u) is concave in (x, y) if and only if for any pair of distinct points (x, y, z, u) and (x, y, z, u) in the domain, we have…”

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

“…To find optimal sequence c i,t , a i,t ∞ t�0 to maximize the expected utility in NSDM (19), the Euler equation and transversality condition for NSDM (19) need to be given.…”

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

“…Atici et al [18] present a dynamic optimal problem from economics and construct a time scale model. Atici et al [19] investigate a perfectforesight utility maximisation problem by using a method for solving the dynamic optimisation problem in which the real-valued function and constraints depend on different times. Atici and Turhan [20] discuss the deterministic dynamic sequence problem on isolated discrete time domains.…”

Section: Introductionmentioning

confidence: 99%

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The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

Huang

Xie

2020

Mathematical Problems in Engineering

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A wealth distribution model on isolated discrete time domains, which allows the wealth to exchange at irregular time intervals, is used to describe the effect of agent’s trading behavior on wealth distribution. We assume that the agents have different degrees of risk aversion. The hyperbolic absolute risk aversion (HARA) utility function is employed to describe the degrees of risk aversion of agents, including decreasing relative risk aversion (DRRA), increasing relative risk aversion (IRRA), and constant relative risk aversion (CRRA). The effect of agent’s expectation on wealth distribution is taken into account in our wealth distribution model, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth status. The Euler equation and transversality condition for the model on isolated discrete time domains are given to prove the existence of the optimal solution of the model. The optimal solution of the wealth distribution model is obtained by using the method of solving the rational expectation model on isolated discrete time domains. A numerical example is given to highlight the advantages of the wealth distribution model.

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“…, and f(x, y, z, u): R 4 ⟶ R + is a concave in (x, y), continuous, and differentiable real-valued function with f y ≤ 0. e discount factor relating to NSDM (19) is…”

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

“…To find optimal sequence c i,t , a i,t ∞ t�0 to maximize the expected utility in NSDM (19), the Euler equation and transversality condition for NSDM (19) need to be given.…”

Section: Nonlinear Stochastic Dynamic Model With a Bivariate Utility mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

Huang

Xie

2020

Mathematical Problems in Engineering

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“…Here we offer a brief introduction to the theory of dynamic equations on time scales. For a more in-depth study of time scales, see Bohner and Peterson's books (Bohner andPeterson, 2001, 2003) as well as some recent contributions (Atici et al, 2011;Kratz et al, 2011;Jackson et al, 2011;.…”

Section: Preliminariesmentioning

confidence: 99%

The Linear Quadratic Tracker on time scales

Böhner

Wintz

2011

IJDSDE

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In this work, we study a natural extension of the Linear Quadratic Regulator (LQR) on time scales. Here, we unify and extend the Linear Quadratic Tracker (LQT). We seek to find an affine optimal control that minimises a cost functional associated with a completely observable linear system. We then find an affine optimal control for the fixed final state case in terms of the current state. Finally we include an example in disturbance/rejection modelling. A numerical example is also included.

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Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

Hilscher

Zeidan

2018

ESAIM: COCV

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The main focus of this paper is to develop a sufficiency criterion for optimality in nonlinear optimal control problems defined on time scales. In particular, it is shown that the coercivity of the second variation together with the controllability of the linearized dynamic system are sufficient for the weak local minimality. The method employed is based on a direct approach using the structure of this optimal control problem. The second aim pertains to the sensitivity analysis for parametric control problems defined on time scales with separately varying state endpoints. Assuming a slight strengthening of the sufficiency criterion at a base value of the parameter, the perturbed problem is shown to have a weak local minimum and the corresponding multipliers are shown to be continuously differentiable with respect to the parameter. A link is established between (i) a modification of the shooting method for solving the associated boundary value problem, and (ii) the sufficient conditions involving the coercivity of the accessory problem, as opposed to the Riccati equation, which is also used for this task. This link is new even for the continuous time setting.

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A utility maximisation problem on multiple time scales

Cited by 3 publications

References 11 publications

The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

The Linear Quadratic Tracker on time scales

Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

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