scholarly journals Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Md. Azizul Baten ◽  
Anton Abdulbasah Kamil
Keyword(s):  
Production Function ◽  
Viscosity Solution ◽  
Solution Method ◽  
Hjb Equation ◽  
Optimal Consumption ◽  
Ramsey Model ◽  
Discounted Utility ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Douglas Production Function

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity solution of the transformed Hamilton-Jacobi-Bellman equation associated with this model. Finally, the optimal consumption policy is derived from the optimality conditions in the HJB equation.

scholarly journals Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Optimal Strategy ◽  
Bellman Equation ◽  
Insurance Company ◽  
Time Value ◽  
Dividend Payments ◽  
Discounted Utility ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.

A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

2018 ◽  
Vol 24 (2) ◽  
pp. 639-676
Author(s):  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Viscosity Solution ◽  
Optimal Control Problems ◽  
Nonlinear Partial Differential Equation ◽  
Infinite Horizon ◽  
Hjb Equation ◽  
Second Order ◽  
Control Problems ◽  
Stochastic Delay ◽  
Hamilton Jacobi Bellman

In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including timetand identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

scholarly journals Fractional Order Version of the Hamilton–Jacobi–Bellman Equation

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Abolhassan Razminia ◽  
Mehdi Asadizadehshiraz ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Optimal Control Problem ◽  
Fractional Order ◽  
Performance Index ◽  
Bellman Equation ◽  
Hjb Equation ◽  
Usual Form ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

We consider an extension of the well-known Hamilton–Jacobi–Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the nonlocality of the fractional order operators, the classical HJB equation, in the usual form, does not hold true for fractional problems. Effectiveness of the proposed technique is illustrated through a numerical example.

scholarly journals Viscosity solution of linear regulator quadratic for degenerate diffusions

2006 ◽  
Vol 2006 ◽  
pp. 1-17
Author(s):  
Md. Azizul Baten
Keyword(s):  
Control Problem ◽  
Viscosity Solution ◽  
Viscosity Solutions ◽  
Hjb Equation ◽  
Linear Regulator ◽  
Degenerate Diffusions ◽  
Hamilton Jacobi Bellman

The paper studied a linear regulator quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We showed the existence of viscosity properties and established a unique viscosity solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions.

Significance of Experience, Farm Size, Quantity of Propagules and Location f or Seaweed Farmers in the Divided Island of Sebatik

2018 ◽  
Vol 9 (9) ◽  
pp. 825-832
Author(s):  
James M. Alin ◽  
◽  
Datu Razali Datu Eranza ◽  
Arsiah Bahron ◽  
◽  
...  
Keyword(s):  
Regression Analysis ◽  
Multiple Regression Analysis ◽  
Multiple Regression ◽  
Production Function ◽  
Weather Conditions ◽  
Education Level ◽  
Farm Size ◽  
Total Production ◽  
Explanatory Factors ◽  
Douglas Production Function

Seaweed-Kappaphycus-Euchema Cottonii and Denticulum species was first cultivated at Sabah side of Sebatik in 2009. By November 2014, sixty one Sabahan seaweed farmers cultivated 122 ha or 3,050 long lines. Thirty Sabahan seaweed farmers in Kampung Pendekar (3.2 m.t dried) and 31 in Burst Point (12.5 m.t dried) produced 16 metric tonnes of dried seaweed contributed 31% to Tawau’s total production (51 m.t). The remaining 69% were from farmers in Cowie Bay that separates Sebatik from municipality of Tawau. Indonesian in Desa Setabu, Sebatik started in 2008. However, the number of Indonesian seaweed farmers, their cultivated areas and production (as well as quality) in Sebatik increased many times higher and faster than the Sabah side of Sebatik. In 2009 more than 1,401 households in Kabupaten Nunukan (including Sebatik) cultivated over 700 ha and have produced 55,098.95 and 116, 73 m.t dried seaweed in 2010 and 2011 respectively. There is a divergence in productions from farming the sea off the same island under similar weather conditions. Which of the eight explanatory factors were affecting production of seaweeds in Sebatik? Using Cobb Douglas production function, Multiple Regression analysis was conducted on 100 samples (50 Sabahan and 50 Indonesian). Results; Variable significant at α = 0.05% are Experience in farming whereas Farm size; Quantity of propagules and Location — Dummy are the variables significant at α 0.01%. Not significant are variables Fuel; Age; Number of family members involved in farming and Education level.

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