Riesz -type integral representations for excessive function of a Markov process are well-known in the potential-theoretic literature. This talk explains the use of these representations for solving stochastic optimization problems, particularly for optimal stopping- and impulse-control-problems. This approach is illustrated by treating the famous optimal investment problem in arbitrary dimension for geometric Brownian motions and certain classes of geometric Lévy processes without using the machinery of local time-space-calculus on manifolds.

The talk is based on [1], [2], and [3].

[1] (with P. Salminen , B. Ta Quoc ) Optimal stopping of strong Markov processes, Stochastic Processes and their Applications, 123, 3, 2013, 1138 -- 1159.

[2] (with P. Salminen ) Riesz representation and optimal stopping - two case studies, 2013, preprint.

[3] A method for pricing American options using semi-infinite linear programming, 2012, to appear in Mathematical Finance.