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Discretionary stopping of one-dimensional Itô diffusions with a staircase reward function

  • Anne Laure Bronstein (a1), Lane P. Hughston (a1), Martijn R. Pistorius (a1) and Mihail Zervos (a1)

Abstract

We consider the problem of optimally stopping a general one-dimensional Itô diffusion X. In particular, we solve the problem that aims at maximising the performance criterion E x [exp(-∫0 τ r(X s )ds)f(X τ)] over all stopping times τ, where the reward function f can take only a finite number of values and has a ‘staircase’ form. This problem is partly motivated by applications to financial asset pricing. Our results are of an explicit analytic nature and completely characterise the optimal stopping time. Also, it turns out that the problem's value function is not C 1, which is due to the fact that the reward function f is not continuous.

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Copyright

Corresponding author

∗∗ Postal address: Department of Mathematics, King's College London, The Strand, London WC2R 2LS, UK.
∗∗∗ Email address: lane.hughston@kcl.ac.uk
∗∗∗∗ Email address: martijn.pistorius@kcl.ac.uk

Footnotes

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Current address: Laboratoire de Probabilités et Modèles Aléotoires, Université Paris 6, 175 rue du Chevaleret, Paris, 75013, France. Email address: albronstein@hotmail.com

∗∗∗∗∗

Current address: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK. Email address: m.zervos@lse.ac.uk

Footnotes

References

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Zervos, M. (2003). A problem of sequential entry and exit decisions combined with discretionary stopping. SIAM J. Control Optimization 42, 397421.

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Discretionary stopping of one-dimensional Itô diffusions with a staircase reward function

  • Anne Laure Bronstein (a1), Lane P. Hughston (a1), Martijn R. Pistorius (a1) and Mihail Zervos (a1)

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