Monte Carlo methods via a dual approach for some discrete time stochastic control problems

Abstract

We consider a class of discrete time stochastic control problems motivated by a range of financial applications. We develop a numerical technique based on the dual formulation of these problems to obtain an estimate of the value function which improves on purely regression based methods. We demonstrate the competitiveness of the method on the example of a gas storage valuation problem.

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Notes

  1. 1.

    We tested rank-\(1\) lattices, see Sect. 5.

  2. 2.

    In Thompson et al. (2009), the continuous time production/injection is described by an ordinary differential equation. The discrete-time formulation is an approximation of the solution to that ODE.

  3. 3.

    Note that, in this paper, the time unit is daily, whereas in Thompson et al. (2009) the time is measured in years.

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Correspondence to Lajos Gergely Gyurkó.

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Gyurkó, L.G., Hambly, B.M. & Witte, J.H. Monte Carlo methods via a dual approach for some discrete time stochastic control problems. Math Meth Oper Res 81, 109–135 (2015). https://doi.org/10.1007/s00186-014-0488-3

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Keywords

  • Stochastic control
  • Dual formulation
  • Monte Carlo
  • Least squares regression