We study isometric cohomogeneity one actions on the (n + 1)-dimensional Minkowski space L n+1 up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on L n+1 whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on L n+1 , n ≥ 3, which are orbit-equivalent on the complement of an n-dimensional degenerate subspace W n of L n+1 and not orbitequivalent on W n . We classify isometric cohomogeneity one actions on L 2 and L 3 up to orbit-equivalence.

Evolutionary Finance (EF) explores financial markets as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some “survive” and some “become extinct”. A central goal is to identify evolutionary stable (in one sense or another) investment strategies. The problem is analyzed in a framework combining stochastic dynamics and evolutionary game theory. Most of the models currently considered in EF assume that asset payoffs are exogenous and depend only on the underlying stochastic process of states of the world. The present work develops a model where the payoffs are endogenous: they depend on the share of total market wealth invested in the asset.

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