Stochastic targets with mixed diffusion processes and viscosity solutions

Bruno Bouchard

Stochastic Processes and their Applications, 2002, vol. 101, issue 2, 273-302

Abstract: Let Zt,z[nu] be a -valued mixed diffusion process controlled by [nu] with initial condition Zt,z[nu](t)=z. In this paper, we characterize the set of initial conditions such that Zt,z[nu] 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.

Keywords: Stochastic; control; Mixed; diffusion; processes; Viscosity; solutions; Super-replication; Mathematical; finance; and; insurance (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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