arXiv research

Derives explicit investment strategy with random endowment.

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …

Extends Gelfand duality to various geometric and analytical categories.

Proves 3D Poincaré duality groups without property (T)

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.

We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a numéraire-based semi-static utility maximization problem with an exponential utility preference. The randomization techniques recently developed in \cite{BDT17} allow us to transform the original proble…

This note provides a novel, simple analysis of the method of conjugate gradients for the minimization of convex quadratic functions. In contrast with standard arguments, our proof is entirely self-contained and does not rely on the existence of Chebyshev polynomials. Another advantage of our development is that it clar…

New method calculates super-hedging prices with transaction costs.

In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that th…

This paper optimizes portfolio management in incomplete markets with stochastic factors, considering periodic wealth evaluations.

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is ext…

Preprint proves quantum coideal Schur-Weyl duality and generalizes Jones-Wenzl projectors.

A result of Jost and Zuo is used to show that for a large class of finite-dimensional hyperkähler quotients, the only L2 harmonic forms lie in the middle dimension, and are of type (k,k) with respect to all complex structures. The argument is extended to some moduli spaces which appear as infinite-dimensional quotients…

We introduce a minorization-maximization approach to optimizing common measures of discovery significance in high energy physics. The approach alternates between solving a weighted binary classification problem and updating class weights in a simple, closed-form manner. Moreover, an argument based on convex duality sho…

This survey paper begins with the description of the duality between arc systems and ribbon graphs embedded in a punctured surface. Then we explain how to cellularize the moduli space of curves in two different ways: using Jenkins-Strebel differentials and using hyperbolic geometry. We also briefly discuss how these tw…

Optimal risk sharing without convex preferences using aggregate convexity.

Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.

Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.

It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solut…

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polyno…

Study homology manifolds using spectral sheaves and spectral six functor formalism.

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Lege…

The paper explores criteria for positivity of forms and proves their strong positivity in specific cases.

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is b…

We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cobordisms. This requires introducing `disorientations' in the category of smoothings and abstract cobordisms between them used in Bar-Natan's …

We prove the qualitative part of Demailly's conjecture on transcendental Morse inequalities for differences of two nef classes satisfying a numerical relative positivity condition on an arbitrary compact Kähler (and even more general) manifold. The result improves on an earlier one by J. Xiao whose constant $4n$ featur…

Proves necessity of at least log2(n) layers to compute maximum of n numbers.

Study scaling limits of utility indifference prices in discretized Bachelier model.

A physicist explores exotic 7-spheres using fibre bundles and instantons.

Proves Poincaré duality for Hopf algebroids with bijective antipode.

We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery period. A quick overview of market data shows a basis risk for this market incom…

We study when a smooth variety $X$, embedded diagonally in its Cartesian square, is the zero scheme of a section of a vector bundle of rank $\dim(X)$ on $X\times X$. We call this the diagonal property (D). It was known that it holds for all flag manifolds ${\rm SL}_n/P$. We consider mainly the cases of proper smooth va…

New proof of chain duality for simplicial complexes.

Introduces Kähler duality between domains in complex space.

Research on dualities in geometric stereotypes.

Study scaling limits for option pricing in trinomial models.

Duality restored in gauge theory, gravity, and string theory models.

Unified proof of four Bavard dualities and new results on quasimorphisms.

We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We presen…

Verma Howe duality connects tensor products of Verma modules to LKB representations.

Cohomological and homological spectral sequences are shown to be isomorphic.

The paper proves T-duality and Hori formulae for winding loop spaces.

Equivariant T-duality connects bundles with twists.

We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $Ω$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of …

The paper establishes T-duality for 2D σ-models with H-flux.

QP perspective on Poisson-Lie T-duality topology changes.

The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.

Unified framework for T-duality in both trivial and non-trivial topologies.