Optimal dynamic investment policies of a value maximizing firm
In: Lecture notes in economics and mathematical systems 330
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In: Lecture notes in economics and mathematical systems 330
In: The Manchester School, Band 78, Heft 1, S. 1-19
ISSN: 1467-9957
In: Journal of economic dynamics & control, Band 31, Heft 5, S. 1672-1696
ISSN: 0165-1889
In: Journal of economic dynamics & control, Band 29, Heft 7, S. 1193-1209
ISSN: 0165-1889
In: Journal of economic dynamics & control, Band 21, Heft 2-3, S. 603-630
ISSN: 0165-1889
In: Journal of economic dynamics & control, Band 17, Heft 1-2, S. 153-180
ISSN: 0165-1889
In: The Rand journal of economics, Band 46, Heft 2, S. 376-408
ISSN: 1756-2171
This article considers investment decisions within an uncertain dynamic and duopolistic framework. Each investment decision involves to determine the timing and the capacity level. The simultaneous analysis of timing and capacity decisions extends work on entry deterrence/accommodation to consider a timing/delay element. We find that, when applying an entry deterrence policy, the first investor, or incumbent, overinvests in capacity for two reasons. First, it delays the investment of the second investor, or entrant. Second, the entrant will invest in less capacity. We also find that greater uncertainty makes entry deterrence more likely.
In: Journal of economics, Band 63, Heft 1, S. 1-23
ISSN: 1617-7134
In: Journal of economic dynamics & control, Band 126, S. 104126
ISSN: 0165-1889
The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation and equilibrium points are in fact equilibrium distributions in the variable of ages. Investments in frontier, as well as non-frontier vintages, are possible. Firstly a general method is developed to compute and study equilibrium points of a wide range of infinite-dimensional, infinite-horizon boundary control problems for linear PDEs with convex criterion, possibly applying to a wide variety of economic problems. Sufficient and necessary conditions for existence of equilibrium points are derived in this general context. In particular, for optimal investment with vintage capital, existence and uniqueness of a long-run equilibrium distribution is proved for general concave revenues and convex investment costs, and analytic formulas are obtained for optimal controls and trajectories in the long run, definitely showing how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions, and suggesting that the same method can be applied in examples yielding the same abstract structure. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal controls and trajectories in the long run. ; The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite-dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distributions, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.
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In: CentER Discussion Paper Series No. 2017-043
SSRN
Working paper
In: Journal of economic dynamics & control, Band 33, Heft 3, S. 583-596
ISSN: 0165-1889
SSRN
In: Environmental Economics and the International Economy; Economy & Environment, S. 89-98
In: Dynamic games and applications: DGA, Band 7, Heft 4, S. 555-577
ISSN: 2153-0793