7 research outputs found

    Regularity of the Optimal Stopping Problem for Jump Diffusions

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    The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in Wp,loc2,1W^{2,1}_{p, loc} with p∈(1,∞)p\in(1, \infty). As a consequence, the smooth-fit property holds.Comment: To Appear in the SIAM Journal on Control and Optimizatio

    Analysis of the optimal exercise boundary of American options for jump diffusions

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    In this paper we show that the optimal exercise boundary/free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at maturity). This differentiability result was established by Yang, Jiang, and Bian [European J. Appl. Math., 17 (2006), pp. 95–127] in the case where the condition rβ‰₯q+λ∫R+ (ezβˆ’1) ν(dz)r\geq q+\lambda\int_{\mathbb{R}_+}\,(e^z-1)\,\nu(dz) is satisfied. We extend the result to the case where the condition fails using a unified approach that treats both cases simultaneously. We also show that the boundary is infinitely differentiable under a regularity assumption on the jump distribution
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