Optimal Stopping of Jump Diffusions

  • Bernt ØksendalEmail author
  • Agnès Sulem
Part of the Universitext book series (UTX)


Fix an open set \(\mathcal S\subset \mathbb {R}^k\) (the solvency region ) and let Y(t) be a jump diffusion in \(\mathbb {R}^k\) given by \( \mathrm{d}Y(t)=b(Y(t))\mathrm{d}t+\sigma (Y(t))\mathrm{d}B(t) +\int _{\mathbb {R}^\ell } \!\gamma (Y(t^-), z) \bar{N}(\mathrm{d}t,\mathrm{d}z),\quad Y(0)=y\!\in \!\mathbb {R}^\ell , \) where \(b:\mathbb {R}^k\rightarrow \mathbb {R}^k\), \(\sigma :\mathbb {R}^k\rightarrow \mathbb {R}^{k\times m}\), and \(\gamma :\mathbb {R}^k\times \mathbb {R}^\ell \rightarrow \mathbb {R}^{k\times \ell }\) are given functions such that a unique solution Y(t) exists (see Theorem  1.19).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Inria Research Center of ParisParisFrance

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