Singular stochastic control and optimal stopping with partial information of jump diffusions
We study partial information, possibly non-Markovian, singular stochastic control of jump diffusions and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. Mathematics Subject Classification 2010: 93E20, 60H07, 60H10, 60HXX, 60J75
Semimartingale Inequalities for The Snell Envelopes
On the finite time interval [0,T] we consider the class of right continuous (with left limits) processes and for each element its Snell envelope, that is the smallest supermartingale bounding X from above. We improve some known properties of the Snell envelopes based on which we prove the main result of this article, namely the inequality where X 1 and X 2 are two arbitrary semimartingales belonging to the space H p P> 1Y 1 and Y 2 are their corresponding Snell envelopes and C p are absolute constants. The key step in proving this result is a bound of the distance in variation between the predictable components of the Snell envelopes Y l and Y 2
Rotational Analysis of the CrO Bands
The (0, 1), (0, 0) and (1, 0) bands of the CrO, which appear in the red and yellow region, are analysed rotationally, and we have been able to show that these bands owe to the transition 5 Π- 5 Π. We have shown the theoretical formulae for the quintet state, which can be applied in the case of nearly (a), and obtained the molecular constants as follows,