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(Research report / Forskningsrapport, 2001)
We give a short introduction to some of the theory and methods involved in stochastic control with partial observation. As an illustration we use the stochastic maximum principle and the Kalman-Bucy filter to solve explicitly ...
(Research report / Forskningsrapport, 2001)
In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We ...
(Research report / Forskningsrapport, 2001)
We give a short introduction to some of the theory and methods involved in We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal ...
(Research report / Forskningsrapport, 2001)
We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations. This is a type of equations which appear as adjoint equations in the maximum principle approach to ...
(Research report / Forskningsrapport, 2001)
A Meyer-Tanaka formula involving weighted local time is derived for fractional Brownian motion and geometric fractional Brownian motion. The formula is applied to the study of the stop-loss-start-gain (SLSG) portfolio in ...
(Research report / Forskningsrapport, 2001)
We prove a sufficient maximum principle for the optimal control of systems described by a quasilinear stochastic heat equation. The result is applied to give a maximum principle solution method for stochastic control ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting, and show the adjoint processes' connections to dynamic programming. The result ...