Type: Preprint
Publication Date: 2022-08-29
Citations: 0
DOI: https://doi.org/10.21203/rs.3.rs-1997495/v1
Abstract In this paper a two-dimensional Brownian motion (modeling the endowment of two companies), absorbed at the boundary of the positive quadrant, with controlled drift, is considered. The volatilities of the Brownian motions are {\em different}. We control the drifts of these processes and allow that both drifts add up to the maximal value of one. Our target is to choose the strategy in a way, s.t. the probability that both companies survive is maximized. It turns out that the state space of the problem is divided into two sets. In one set the first company gets the full drift, and in the other set the second one. We describe some topological properties of these sets and their separating curve.
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