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Stochastic Target with Mixed diffusion processes

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Date
2002
Dewey
Probabilités et mathématiques appliquées
Sujet
Mathematical finance and insurance; Stochastic control; Stochastic target
Journal issue
Stochastic Processes and their Applications
Volume
101
Number
2
Publication date
10-2002
Article pages
273-302
DOI
http://dx.doi.org/10.1016/S0304-4149(02)00129-1
URI
https://basepub.dauphine.fr/handle/123456789/1790
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
Let Zt,zν be a Image -valued mixed diffusion process controlled by ν with initial condition Zt,zν(t)=z. In this paper, we characterize the set of initial conditions such that Zt,zν can be driven above a given stochastic target at time T by proving that the corresponding value function is a discontinuous viscosity solution of a variational partial differential equation. As applications of our main result, we study two examples: a problem of optimal insurance under self-protection and a problem of option hedging under jumping stochastic volatility where the underlying stock pays a random dividend at a fixed date.

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