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Stochastic control on the half-line and applications to the optimal dividend/consumption problem

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  • Dariusz Zawisza

Abstract

We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations has smooth solution. The aforementioned result is used to solve the optimal dividend and consumption problem. In the proof we use a fixed point type argument, with an operator which is based on the stochastic representation for a linear equation.

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  • Dariusz Zawisza, 2017. "Stochastic control on the half-line and applications to the optimal dividend/consumption problem," Papers 1703.07339, arXiv.org, revised Jul 2018.
    • Handle: RePEc:arx:papers:1703.07339
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    2. Ralf Korn & Holger Kraft, 2003. "Optimal Portfolios With Defaultable Securities A Firm Value Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 793-819.
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