The paper investigates quadratic hedging in a general semimartingale market that does not necessarily contain risk-free asset. An equivalence result for with and without numeraire change is established. This permits direct computation of the optimal strategy choosing reference asset and/or performing change. New explicit expressions strategies are obtained, featuring use oblique projections pro...

In this paper, we consider a closed Riemannian manifold $$M^{n+1}$$ with dimension $$3\le n+1\le 7$$ , and compact Lie group G acting as isometries on M cohomogeneity at least 3. Suppose the union of non-principal orbits $$M{\setminus } M^{reg}$$ is smooth embedded submanifold most $$n-2$$ . Then for any $$c\in \mathbb {R}$$ show existence nontrivial, smooth, closed, almost embedded, G-invarian...

We develop a theory of mean-square random invariant manifolds for dynamical systems generated by stochastic differential equations. This is applicable to partial equations driven nonlinear noise. The existence unstable proved the Lyapunov-Perron method based on backward equation involving conditional expectation with respect filtration. stable sets also established but remains open.

Abstract It is known that if a bivariate mean K symmetric, continuous and strictly increasing in each variable, then for every M there unique $$N\,$$ N such invariant with respect to the mean-type mapping $$\left( M,N\right) ,$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><...

Using 1-twist rim surgery, we construct infinitely many smoothly embedded, orientable surfaces in the 4-ball bounding a knot 3-sphere that are pairwise topologically isotopic, but not ambient diffeomorphic. We distinguish using maps they induce on perturbed sutured Floer homology. Along way, show cobordism map induced by an ascending surface Weinstein preserves transverse invariant