Stochastics and Finance Seminar: Chunxi Jiao -- Computable primal and dual bounds for some stochastic control problems

Speaker: Chunxi Jiao (University of Sydney)  

Title: Computable primal and dual bounds for some stochastic control problems

We investigate the linear programming framework for stochastic control with a view 
towards the numerical implementation (Lasserre’s hierarchy) for obtaining pointwise 
bounds and global bounding functions for the value function. The primal minimisation 
corresponds to the well-studied moment problem based upon a set of necessary equality 
constraints on the occupation and boundary measures, whereas the dual maximisation is 
built on a set of sufficient inequality constraints on the test polynomial function 
with a flexible choice of optimality criteria. Under suitable technical conditions, 
optimised bounds are convergent to the value function as the polynomial degree tends to 
infinity. The dual maximisation is particularly effective as its single implementation 
yields a remarkably tight global bound in the form of polynomial function over the whole 
problem domain, and with a suitable objective function, one may improve the global bound 
on regions of interest. 

http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html