1,928 research outputs found
Stochastic partial differential equations driven by Levy space-time white noise
In this paper we develop a white noise framework for the study of stochastic
partial differential equations driven by a d-parameter (pure jump) Levy white
noise. As an example we use this theory to solve the stochastic Poisson
equation with respect to Levy white noise for any dimension d. The solution is
a stochastic distribution process given explicitly. We also show that if d\leq
3, then this solution can be represented as a classical random field in L2(\mu
), where \mu is the probability law of the Levy process.
The starting point of our theory is a chaos expansion in terms of generalized
Charlier polynomials. Based on this expansion we define Kondratiev spaces and
the Levy Hermite transform
Maximum principles for jump diffusion processes with infinite horizon
We prove maximum principles for the problem of optimal control for a jump
diffusion with infinite horizon and partial information. The results are
applied to partial information optimal consumption and portfolio problems in
infinite horizon
A maximum principle for infinite horizon delay equations
We prove a maximum principle of optimal control of stochastic delay equations
on infinite horizon. We establish first and second sufficient stochastic
maximum principles as well as necessary conditions for that problem. We
illustrate our results by an application to the optimal consumption rate from
an economic quantity
Sensitivity analysis in a market with memory
A general market model with memory is considered in terms of stochastic
functional differential equations. We aim at representation formulae for the
sensitivity analysis of the dependence of option prices on the memory. This
implies a generalization of the concept of delta.Comment: Withdrawn by the authors due to an error in equation (2.6). A new
work is in preparatio
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