81 research outputs found
Optimal decision under ambiguity for diffusion processes
In this paper we consider stochastic optimization problems for an ambiguity
averse decision maker who is uncertain about the parameters of the underlying
process. In a first part we consider problems of optimal stopping under drift
ambiguity for one-dimensional diffusion processes. Analogously to the case of
ordinary optimal stopping problems for one-dimensional Brownian motions we
reduce the problem to the geometric problem of finding the smallest majorant of
the reward function in a two-parameter function space. In a second part we
solve optimal stopping problems when the underlying process may crash down.
These problems are reduced to one optimal stopping problem and one Dynkin game.
Examples are discussed
Convergence of switching diffusions
This paper studies the asymptotic behavior of processes with switching. More
precisely, the stability under fast switching for diffusion processes and
discrete state space Markovian processes is considered. The proofs are based on
semimartingale techniques, so that no Markovian assumption for the modulating
process is needed
On the Solution of General Impulse Control Problems Using Superharmonic Functions
In this paper, a characterization of the solution of impulse control problems
in terms of superharmonic functions is given. In a general Markovian framework,
the value function of the impulse control problem is shown to be the minimal
function in a convex set of superharmonic functions. This characterization also
leads to optimal impulse control strategies and can be seen as the
corresponding characterization to the description of the value function for
optimal stopping problems as a smallest superharmonic majorant of the reward
function. The results are illustrated with examples from different fields,
including multiple stopping and optimal switching problems
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