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Large time asymptotic problems for optimal stochastic control with superlinear cost

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  • Ichihara, Naoyuki
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911003139
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1248-1275

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1248-1275

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    Related research

    Keywords: Stochastic control; Large time behavior; Hamilton–Jacobi–Bellman equation; Ergodic control;

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    1. M. R. Grasselli & T. R. Hurd, 2007. "Indifference Pricing and Hedging for Volatility Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 303-317.
    2. Hiroaki Hata & Hideo Nagai & Shuenn-Jyi Sheu, 2010. "Asymptotics of the probability minimizing a "down-side" risk," Papers 1001.2131, arXiv.org.
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