We propose a new definition for tameness within the model of security prices as Itô processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims...

A visceral structure on M is given by a definable base for uniform topology its universe in which all basic open sets are infinite and any subset X⊆M has nonempty interior. Assuming only viscerality, we show that the satisfy some desirable topological tameness conditions. For example, function f:M→M finite set of discontinuities; f:Mn→Mm continuous nonnempty set; assuming choice, obtain cell de...

1. Morley, Marsh, Baldwin/Lachlan, Zilber; and Macintyre 2 2. The Borovik Program: CFSG and tameness 3 2.1. The setting: tame or not 3 2.2. The basic framework: even, odd, mixed, degenerate 4 3. Mixed type 5 3.1. Strong and weak embedding 5 3.2. Toward weak embedding: U(G) 6 3.3. The subgroups B(G) and D(G) 6 3.4. The strategy 7 3.5. The curious incident of the dog in the night 8 3.6. Weak embe...

The main theorem of this paper states that if M is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the rank of H1(M ;Z/2Z) is at most 10. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geomet...