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Anastasis Kratsios

Publications and source records attributed to Anastasis Kratsios.

80 records · Page 5Linked to original sources
arXiv2019

Partial Uncertainty and Applications to Risk-Averse Valuation

This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff of derivative security in a complete financial market, its R-conditioning with respect to the risk-neutral measure is interpreted as its risk-averse value. The optimization problem defining the optimization R-conditioning is shown to be well-posed. We show that the R-conditioning operators can be used to approximate a large class of sublinear expectations to arbitrary precision. We then introduce a novel numerical algorithm for computing the R-conditioning. This algorithm is shown to be strongly convergent. Implementations are used to compare the risk-averse value of a Vanilla option to its traditional risk-neutral value, within the Black-Scholes-Merton framework. Concrete connections to robust finance, sensitivity analysis, and high-dimensional estimation are all treated in this paper.

q-fin.RM↗
arXiv2019

A Lower-Bound on the Hochschild Cohomological Dimension

A concrete lower-bound for the Hochschild cohomological dimension of a commutative $k$-algebra, in terms of three other homological invariants is obtained. This result is then used to show that most $k$-algebras fail to be quasi-free, even if they are smooth. This result generalizes a result of \cite{cuntz1995algebra} to the case where the base-ring is no longer $\cc$ but can be any commutative ring with unity.

math.RA↗
arXiv2019

Hochschild Cohomological Dimension is Not Upper Semi-Continuous

It is shown that the Hochschild Cohomological dimension of an associative algebra is not an upper-semi continuous function, showing the semi-continuity theorem is no longer valid for non-commutative algebras. A family of $\mathbb{C}$ exhibits this-algebras parameterized by $\mathbb{C}$ all but one of which has Hochschild cohomological dimension $2$ and the other having Hochschild cohomological dimension $1$.

math.RA↗
arXiv2019

The Entropic Measure Transform

We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the EMT provides economic interpretations as a maximization of returns subject to a penalty for removing financial risk as expressed through the aggregate relative entropy. The EMT is shown to extend the optimal stochastic control characterization of default-free bond prices of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013). These methods are illustrated numerically with an example in the defaultable bond setting.

q-fin.MF↗
arXiv2018

Non-Euclidean Conditional Expectation and Filtering

A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. This gives computationally tractable filtering equations for the dynamics of the intrinsic conditional expectation of a manifold-valued signal and is used to obtain accurate numerical forecasts of efficient portfolios by incorporating their geometric structure into the estimates.

q-fin.MF↗
arXiv2014

Noncommutative Algebra and Noncommutative Geometry

Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative algebra's smoothness. The second part of this text is then, devoted to the approximating of properties of nc. schemes through the properties of two uniquely determined (classical) schemes estimating the nc. scheme in question in a maximal way from the inside and through the minimal scheme approximating the nc. scheme in question from the outside. The very brief final par of this exposition, aims to understand and distil the properties at work in constructing any "scheme-like" object over an "appropriate" category, purely out of philosophical interest.

math.RA↗
arXiv2014

Adjoinable Homology

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext functors to an arbitrary coalgebra. A new homology theory theory is then built therefrom and is shown to exhibit certain duality relations to the Hochschild cohomology of certain coalgebras. Lastly, a certain exceptional type of coalgebra is introduced and it is used to make explicit connections between this new homology theory and the continuous cohomology of this exceptional algebra's pro-finite dual algebra.

math.RA↗