Stochastic control problems for systems driven by normal martingales

Details Stochastic control problems for systems driven by normal martingales Stochastic control problems for systems driven by normal martingales

2007-06-27

arxiv.org/abs/0706.4018v2

Annals of Applied Probability 2008, Vol. 18, No. 2, 632-663

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AAP467 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP467

In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general insurance models to queueing theory. The main novel point of such a control problem is that by changing the jump size of the system, one essentially changes the type of the driving martingale. Such a feature does not seem to have been investigated in any existing stochastic control literature. We shall first provide a rigorous theoretical foundation for the control problem by establishing an existence result for the multidimensional structure equation on a Wiener--Poisson space, given an arbitrary bounded jump size control process; and by providing an auxiliary counterexample showing the nonuniqueness for such solutions. Based on these theoretical results, we then formulate the control problem and prove the Bellman principle, and derive the corresponding Hamilton--Jacobi--Bellman (HJB) equation, which in this case is a mixed second-order partial differential/difference equation. Finally, we prove a uniqueness result for the viscosity solution of such an HJB equation.

Affiliated with

Also associated with

No associations

Rating

Stochastic control problems for systems driven by normal martingales does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stochastic control problems for systems driven by normal martingales, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic control problems for systems driven by normal martingales will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-255881