Large time asymptotic problems for optimal stochastic control with superlinear cost
Stochastic Processes and their Applications Volume 122 Issue 4
Page 1248-1275
published_at 2012
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| File | |
| Title ( eng ) |
Large time asymptotic problems for optimal stochastic control with superlinear cost
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| Creator |
Ichihara Naoyuki
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| Source Title |
Stochastic Processes and their Applications
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| Volume | 122 |
| Issue | 4 |
| Start Page | 1248 |
| End Page | 1275 |
| Abstract |
The paper is concerned with stochastic control problems of finite time horizon whose running cost function is of superlinear growth with respect to the control variable. We prove that, as the time horizon tends to infinity, the value function converges to a function of variable separation type which is characterized by an ergodic stochastic control problem. Asymptotic problems of this type arise in utility maximization problems in mathematical finance. From the PDE viewpoint, our results concern the large time behavior of solutions to semilinear parabolic equations with superlinear nonlinearity in gradients. (c) 2011 Elsevier B.V. All rights reserved.
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| Keywords |
Stochastic control
Large time behavior
Hamilton-Jacobi-Bellman equation
Ergodic control
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| NDC |
Information science [ 007 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Elsevier B.V.
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| Date of Issued | 2012 |
| Rights |
(c) 2011 Elsevier B.V. All rights reserved.
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0304-4149
[DOI] 10.1016/j.spa.2011.12.005
[NCID] AA00436340
[DOI] http://dx.doi.org/10.1016/j.spa.2011.12.005
[URI] http://www.elsevier.com/locate/spa
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