Abstract: The paper is concerned with Bellman’s inclusions for the value function of the
optimal stopping for a Markov process on a complete separable metric space
The author investigates a connection between seemingly unrelated objects:
excessive measures, differential inclusions and optimal stopping. Conditions are
given under which an evolutionary Bellman inclusion has a strong or weak solution
in the Hilbert space where is an excessive measure for The
solution is identified with the value function of a stopping problem. The stationary
Bellman inclusion is treated as well. Specific examples of diffusions with jumps
and infinite-dimensional diffusions are discussed. Excessivity of the measure
plays an essential role in the development. The results are then applied to pricing
American options both in finite and infinite dimensions recently investigated by
Zhang [32], Mastroeni and Matzeu [20], [21], and Gtarek and Musiela [11].
on a complete separable metric space
The author investigates a connection between seemingly unrelated objects:
excessive measures, differential inclusions and optimal stopping. Conditions are
given under which an evolutionary Bellman inclusion has a strong or weak solution
in the Hilbert space 
where 
is an excessive measure for 
The
solution is identified with the value function of a stopping problem. The stationary
Bellman inclusion is treated as well. Specific examples of diffusions with jumps
and infinite-dimensional diffusions are discussed. Excessivity of the measure 
plays an essential role in the development. The results are then applied to pricing
American options both in finite and infinite dimensions recently investigated by
Zhang [32], Mastroeni and Matzeu [20], [21], and G
tarek and Musiela [11].