arXiv research

Develops a new method to study algebraic tangent cones of sheaves using valuations.

This article is the third part of the series of articles where the theory of valuations on manifolds is constructed. In math.MG/0503399 the notion of a smooth valuation on a manifold was introduced. The goal of this article is to put a canonical multiplicative structure on the space of smooth valuations on general mani…

We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…

New framework values football players based on in-game interactions.

This paper applies quantum theory to cost accounting, focusing on WIP valuation.

Proves hard Lefschetz theorem and Hodge-Riemann relations for convex valuations.

The dimensions of the spaces of $k$-homogeneous $\mathrm{Spin}(9)$-invariant valuations on the octonionic plane are computed using results from the theory of differential forms on contact manifolds as well as octonionic geometry and representation theory. Moreover, a valuation on Riemannian manifolds of particular inte…

Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant valuations, generalizing Hadwiger's classification of Euclidean isometry-invari…

Framework for realistic insurance liability valuation.

An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are discussed.

In this paper, we endow the space of continuous translation invariant valuation on convex sets generated by mixed volumes coupled with a suitable Radon measure on tuples of convex bodies with two appropriate norms. This enables us to construct a continuous extension of the convolution operator on smooth valuations to n…

In this paper, within the framework of uncertainty theory, the valuation of equity warrants is investigated. Different from the methods of probability theory, the equity warrants pricing problem is solved by using the method of uncertain calculus. Based on the assumption that the firm price follows an uncertain differe…

New proof confirms operations on constructible functions match theory.

This paper addresses credit valuation adjustment with a new closeout convention.

We develop a unified valuation theory that incorporates credit risk (defaults), collateralization and funding costs, by expanding the replication approach to a generality that has not yet been studied previously and reaching valuation when replication is not assumed. This unifying theoretical framework clarifies the re…

Improved KNN data valuation method with reduced computation time.

This work simplifies data valuation for LLMs using Shapley value computation.

This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…

Optimal pricing strategy for unknown valuation models with noisy feedback.

Averaging problems are ubiquitous in Finance with the valuation of the so-called Asian options on arithmetic averages as their most conspicuous form. There is an abundance of numerical work on them, and their stochastic structure has been extensively studied by Yor and his school. However, the analytical structure of t…

Alesker has introduced the space $\mathcal V^\infty(M)$ of {\it smooth valuations} on a smooth manifold $M$, and shown that it admits a natural commutative multiplication. Although Alesker's original construction is highly technical, from a moral perspective this product is simply an artifact of the operation of inters…

In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of important subclasses of valuation functions that express no-complementarities. Our main…

Permutation-equivariant neural networks improve auction mechanisms by reducing regret and sample complexity.

Probabilistic theory counts intersections in Riemannian spaces.

Models to price long term loans in the securities lending business are developed. These longer horizon deals can be viewed as contracts with optionality embedded in them. This insight leads to the usage of established methods from derivatives theory to price such contracts. Numerical simulations are used to demonstrate…

The Weyl tube theorem is extended to Kähler manifolds.

Following the approach of standard filtering theory, we analyse investor-valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold the…

New method for risk quantification using quantile processes and measure distortions.

Paper introduces new actuarial-consistent valuations for insurance liabilities.

Non-uniqueness found in option valuation for certain α values.

Study optimizes insurance liability cash flows with regulatory capital requirements.

This paper addresses recalibration issues in hedging callable assets, proposing a new risk-adjusted approach.

The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself. Yields vary across different investment opportunities and their interrelations are …

Paper recovers uncertainty from dynamic valuation rules.

The abstract reviews Markov models in life insurance surplus.

Study convolution of invariant valuations on Lie groups.

We develop extensions to auction theory results that are useful in real life scenarios. 1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance related auction settings since asset prices are usually non-negative. 2. We formulat…

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Brokerage algorithm learns from context to minimize trading regret.

Market valuation duration is 175 years, but drops to 46 years during crises.

Paper simplifies default process modeling and credit valuation.

An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables, we derive a valuation framework by the expected marginal gain and marginal loss i…

Business cycles affect startup valuations, both directly and indirectly.

Classification of SL(n) covariant valuations on Orlicz spaces.

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and com…

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices …

Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.

Study evaluates valuation models for UK companies using case studies.