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Singular stochastic control in the presence of a state-dependent yield structure

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  • Alvarez, Luis H. R.

Abstract

We consider the determination of the optimal singular stochastic control for maximizing the expected cumulative revenue flows in the presence of a state-dependent marginal yield measuring the instantaneous returns accrued from irreversibly exerting the singular policy. As in standard models of singular stochastic control, the underlying stochastic process is assumed to evolve according to a regular linear diffusion. We derive the value of the optimal strategy by relying on a combination of stochastic calculus, the classical theory of diffusions, and non-linear programming. We state a set of usually satisfied conditions under which the optimal policy is to reflect the controlled process downwards at an optimal threshold satisfying an ordinary first-order necessary condition for an optimum. We also consider the comparative static properties of the value and state a set of sufficient conditions under which it is concave. As a consequence, we are able to state a set of sufficient conditions under which the sign of the relationship between the volatility of the process and the value is negative.

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Bibliographic Info

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

Volume (Year): 86 (2000)
Issue (Month): 2 (April)
Pages: 323-343

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Handle: RePEc:eee:spapps:v:86:y:2000:i:2:p:323-343

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Related research

Keywords: Singular stochastic control Value function Optimal reflection Green-kernel Linear diffusion;

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Cited by:
  1. Zhuo Jin & George Yin & Chao Zhu, 2011. "Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation," Papers 1111.2584, arXiv.org.
  2. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
  3. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," CORE Discussion Papers 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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