arXiv research

Analyzes complex structure deformations using cohomology contraction methods.

Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.

A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the admissible set. Often, such contracts specify that the holder exert control at a…

Let H denote the standard one-point completion of a real Hilbert space. Given any non-trivial proper sub-set U of H one may define the so-called `Apollonian' metric d_U on U. When U \subset V \subset H are nested proper subsets we show that their associated Apollonian metrics satisfy the following uniform contraction p…

Develops a contraction framework for MCMC mixing rates.

New Q-learning method achieves optimal sample complexity for average-reward problems.

Fair insurance contracts are designed to handle default risk using cooperative game theory.

In this paper we give three applications of a method to prove h-principles on closed manifolds. Under weaker conditions this method proves a homological h-principle, under stronger conditions it proves a homotopical one. The three applications are as follows: a homotopical version of Vassiliev's h-principle, the contra…

Optimal insurance contract limits insurer's risk exposure variance.

Proves existence and uniqueness of mean curvature flow.

New proofs of h-principles in contact 3-manifolds.

The paper solves an insurance problem using mean-variance and rank-dependent utility theory.

This paper investigates Pareto optimal (PO, for short) insurance contracts in a behavioral finance framework, in which the insured evaluates contracts by the rank-dependent utility (RDU) theory and the insurer by the expected value premium principle. The incentive compatibility constraint is taken into account, so the …

The paper explores optimal insurance contracts using various deviation measures.

We consider geometric flow equations for contracting and expanding normal velocities, including powers of the Gauss curvature, of the mean curvature, and of the norm of the second fundamental form, and ask whether - after appropriate rescaling - closed strictly convex surfaces converge to spheres. To prove this, many a…

A new method to break down insurance costs into risk and uncertainty.

New method enhances graph neural networks using contractions and hourglass persistence.

By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in …

Two-layer model studies reinsurance contracts and competition between insurer and reinsurers.

Study semiclassical measures on complex hyperbolic quotients, identifying measure supports.

Study on curve shortening flow with boundary conditions, proving convergence or contraction.

For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy le…

The article extends previous work on contracting convex hypersurfaces by nonhomogeneous curvature functions.

Study random walks on CAT(0) spaces with contracting elements, proving limit laws.

Optimal insurance contracts are designed to screen risk preferences and risk types under asymmetric information.

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement upon this iterative algorithms in terms of their respective performance metrics an…

Extends online learning to metric spaces using exponential weights.

We develop a pricing rule for life insurance under stochastic mortality in an incomplete market by assuming that the insurance company requires compensation for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our valuation formula satisfies a number of desirable properties, many of which it shares w…

Tackling climate change is at the top of many agendas. In this context, emission trading schemes are considered as promising tools. The regulatory framework for an emission trading scheme introduces a market for emission allowances and creates a need for risk management by appropriate financial contracts. In this work,…

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein d…

The paper tackles robust control for insurance contracts under uncertain transition rates.

Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay constraints. The server receives all its information about the problem instance from the wo…

Sharp comparison theorems are derived for all eigenvalues of the (weighted) Laplacian, for various classes of weighted-manifolds (i.e. Riemannian manifolds endowed with a smooth positive density). Examples include Euclidean space endowed with strongly log-concave and log-convex densities, extensions to $p$-exponential …

This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…

New stability theory for Sinkhorn semigroups with explicit decay rates.

Developing a non-symmetric strainer theory for spaces with non-negative curvature beyond Alexandrov geometry.

Study non-negative curvature Markov chains, proving entropy contraction.

New approach to quantify posterior concentration rates using Wasserstein dynamics.

Prediction markets and crypto options show persistent pricing gaps.

We show short-time existence for curves driven by curve diffusion flow with a prescribed contact angle $α\in (0, π)$: The evolving curve has free boundary points, which are supported on a line and it satisfies a no-flux condition. The initial data are suitable curves of class $W_2^γ$ with $γ\in (\tfrac{3}{2}, 2]$. For …

Study of insurance market equilibria with risk-averse policyholders.

Retirement gratuity is the money companies typically pay their employees at the end of their contracts or at the time of leaving the company. It is a defined benefit plan and is often given as an alternative to a pension plan. In Botswana, there is now a new pattern whereby companies give their employees the option to …

Extends option pricing model to incorporate market factor dynamics.

Maximizes coding rate difference for robust, discriminative features.

Unified tensor network formalism for combining neural and symbolic AI.

The paper explores coalescent contractions in contractible spaces, providing criteria and examples.

Bayesian method improves predictions in overparameterized nonlinear regression.

Large deviations theory applied to policy gradient methods.