Impulse control problem on finite horizon with execution delay

By Benjamin Bruder, Huyen Pham. 2007

58 citations recorded by the source corpus.

We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before the effective execution of the first one. This is motivated by financial applications in the trading of illiquid assets such as hedge funds. We show that the value functions for such control problems satisfy a suitable version of dynamic programming principle in finite dimension, which takes into account the past dependence of state process through the pending orders. The corresponding Bellman partial differential equations (PDE) system is derived, and exhibit some peculiarities on the coupled equations, domains and boundary conditions. We prove a unique characterization of the value functions to this nonstandard PDE system by means of viscosity solutions. We then provide an algorithm to find the value functions and the optimal control. This easily implementable algorithm involves backward and forward iterations on the domains and the value functions, which appear in turn as original arguments in the proofs for the boundary conditions and uniqueness results.

Subfields: Control and Systems Engineering, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/40ea74a2b237371267058f1f684a7268e7caf993

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In Control and Systems Engineering

  1. Agnès Sulem
  2. Bernt Øksendal

In Finance

  1. Agnès Sulem
  2. Bernt Øksendal
  3. B. Larssen
  4. David Nualart
  5. Fred Espen Benth
  6. Yasushi Ishikawa
  7. Peter Imkeller
  8. Frank Norbert Proske

In Modeling and Simulation

  1. Bernt Øksendal

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