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Stochastic Target with Mixed diffusion processes

Bouchard, Bruno (2002), Stochastic Target with Mixed diffusion processes, Stochastic Processes and their Applications, 101, 2, p. 273-302. http://dx.doi.org/10.1016/S0304-4149(02)00129-1

Type
Article accepté pour publication ou publié
Date
2002
Journal name
Stochastic Processes and their Applications
Volume
101
Number
2
Pages
273-302
Publication identifier
Metadata
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Author(s)
Bouchard, Bruno
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.
Subjects / Keywords
Mathematical finance and insurance; Stochastic control; Stochastic target