Controlled risk processes in discrete time: Lower and upper approximations to the optimal probability of ruin [An article from: Insurance Mathematics and Economics]

This digital document is a journal article from Insurance Mathematics and Economics, published by Elsevier in 2005. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
We consider the controlled random walk as a flexible model of risk process which takes into account the possibility of intervention of the insurer. We derive a method of approximating the optimal probability of ruin from below and from above. The approximations are based on iterations of the Bellman operator. To initialize the sequence of upper approximations we can use the Lundberg bound or another upper bound on the probability of ruin.