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(Research report / Forskningsrapport, 2009)
In the first part of the paper, we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus ...
(Research report / Forskningsrapport, 2009)
In this paper we study the Cauchy problem for the wave equation with space-time Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C2-solution, ...
(Research report / Forskningsrapport, 2009)
In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy type of noise. We use techniques of Malliavin calculus and forward ...
(Research report / Forskningsrapport, 2009)
(Research report / Forskningsrapport, 2009)
In this paper we introduce Skorohod-semimartingales as an expanded concept of classical semimartingales in the setting of Lévy processes. We show under mild conditions that Skorohod-semimartingales similarly to semimartingales ...
(Research report / Forskningsrapport, 2009)
In this paper, we study backward stochastic differential equations with respect to general filtrations. The results are used to find the optimal consumption rate for an insider from a cash flow modeled as a generalized ...
(Research report / Forskningsrapport, 2009)
We study an optimal stopping problem for a stochastic differential equation with delay driven by a Lévy noise. Approaching the problem by its infinite-dimensional representation, we derive conditions yielding an explicit ...