A DNS-curve in a two-state capital accumulation model: a numerical analysis

Haunschmied, J.L.; Kort, Peter M.; Hartl, Richard F.; Feichtinger, Gustav

doi:10.1016/s0165-1889(01)00070-7

“…The following problem from Haunschmied et al (2003) is a 2d variant of an investment problem of the firm where the control variable is the change of investment rather than investment itself as in the usual case. The payoff function is here given by…”

Section: A 2d Model With Multiple Domains Of Attractionmentioning

confidence: 99%

“…The vector field shows that there is a bifurcation of the dynamics, where the trajectories go either to the low level steady state or high level steady states. This bifurcation line has been called a Skiba curve in Haunschmied et al (2003). The above vector field was generated by DP 19 and serves as a benchmark for assessing the quality of the NMPC solutions.…”

Section: Figure 53: Vector Field Of the Model With Multiple Attractorsmentioning

confidence: 99%

Using nonlinear model predictive control for dynamic decision problems in economics

Grüne

¹

,

Semmler

²

,

Stieler

³

2015

Journal of Economic Dynamics and Control

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This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems.

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“…6 For the latter see Bréchet et al (2012) 7 See Feichtinger et al (2001) and Haunschmied et al (2003). 8 In the latter type of models a convex-concave production function arises which leads to thresholds separating paths to low per capita income (poor) countries and high per capita income (rich) countries, see Skiba (1978) and Azariadis and Drazen (1990).…”

Section: Problem Formulationmentioning

confidence: 99%

Using Nonlinear Model Predictive Control for Dynamic Decision Problems In Economics

Grüne

¹

,

Semmler

²

,

Stieler

³

2013

View full text Add to dashboard Cite

This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems.

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“…Compared to the mild recession case, an additional steady state Â II ,p II arises, which results in history dependent behavior, as illustrated in Figure 5. In particular, Â II ,p II acts as a weak Skiba point (see, e.g., Grass et al, 2008;Caulkins et al, 2007;Haunschmied et al, 2003) , below which reputation and hence demand is so low that the firm acts as if the recession is severe, and above which reputation and hence demand is so high that the firm acts as if the recession is mild. If the brand image exceedsÂ II , the optimal trajectories always converge to the steady stateÂ I in a monotonic way, so the firm lives on forever and bankruptcy never occurs.…”

Section: Intermediate Recessionmentioning

confidence: 99%

Optimal pricing of a conspicuous product during a recession that freezes capital markets

Caulkins¹,

Feichtinger²,

Grass³

et al. 2011

Journal of Economic Dynamics and Control

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This paper considers the problem of how to price a conspicuous product when the economy is in a recession that disrupts capital markets. A conspicuous product in this context is a luxury good for which demand is increasing in brand image. Brand image here means the ability of a consumer to impress observers by conspicuously displaying consumption of the good. Brand image is built up when the good is priced high enough to make it exclusive, and eroded if the good is discounted.Recession is modeled as having two effects: it reduces demand and it freezes capital markets so borrowing is not possible. In pricing the conspicuous product the firm faces the following trade-off. Reducing price helps maintain sales volume and cash flow in the face of reduced demand, but it also damages brand image and thus long term demand. Email address: kort@uvt.nl (P.M. Kort) September 13, 2010 interventions in capital markets and for timing of mergers and acquisitions. Preprint submitted to JEDC

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A DNS-curve in a two-state capital accumulation model: a numerical analysis

Cited by 28 publications

References 14 publications

Using nonlinear model predictive control for dynamic decision problems in economics

Using nonlinear model predictive control for dynamic decision problems in economics

Using Nonlinear Model Predictive Control for Dynamic Decision Problems In Economics

Optimal pricing of a conspicuous product during a recession that freezes capital markets

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