| Autor: |
Dieter Grass, Tatiana Kiseleva, Florian Wagener |
| Přispěvatelé: |
Equilibrium, Expectations & Dynamics / CeNDEF (ASE, FEB) |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Communications in Nonlinear Science & Numerical Simulation, 22(1-3), 38-54. Elsevier |
| ISSN: |
1007-5704 |
| Popis: |
We derive small-noise approximations of the value function of stochastic optimal control problems over an unbounded domain and use these to perform a bifurcation analysis of these problems. The corresponding zero-noise problems may feature indifference (shock, Skiba) points, that is, points of non-differentiability of the value function. Small-noise expansions are obtained in regions of regularity by a singular perturbation analysis of the stochastic Hamilton–Jacobi–Bellman equation; the expansions are matched at the boundaries of these regions to obtain an approximation over the whole state space. From this approximation, a functional geometric invariant is computed: in the presence of zero-noise indifference points, this invariant is multimodal. Regime switching thresholds of the optimally controlled dynamics are defined as those critical points where the invariant takes a local minimum. A change in the number of thresholds is a bifurcation of the dynamics. The concepts are applied to analyse the stochastic lake model. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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