Raymond Brummelhuis
Mittwoch, 18.01.2012
University of London, Birkbeck College
Deterministic and stochastic continuous time models for storage problems
Abstract
We consider simple deterministic and stochastic continuous time models for gas storage (or
storage of other types of commodities) which we examine from a variety of viewpoints: (1)
dynamic programming and HJB equation, (2) reformulation as a path-wise stochastic optimal
control problem following Chris Rogers, (3) Pontryagin's maximum principle and its variant
for stochastic control problems. The aim (not yet achieved) is to look for solutions which are
as explicit as possible, notably for the deterministic problem, and from there try and
construct effective approximations for the stochastic model, in the limit of small effective
volatility. A major problem is posed by the state space constraints in the form of minimum
and maximum reservoir level, which translate into appropriate boundary conditions, in the
form of differential inequalities, for the HJB equation. In certain special cases (deterministic
perpetual storage, certain perpetual storage models with GBM price) these have trivial
explicit solutions.
http://www.lef.wiwi.uni-due.de/forschung/seminarreihe-energy-finance/wintersemester-1112/