Study on ruin probabilities for Lévy processes with light-tailed jumps.
problem Determining bounds on ruin probabilities for Lévy processes.
method Analyzing the Laplace exponent of the Lévy process to find bounds on ruin probabilities.
result Identification of a new case not previously considered in the literature.
Study on Parisian ruin for a refracted Lévy process with adaptive premium rate.
problem Investigating the probability of Parisian ruin for a Lévy insurance risk process with a refracted premium rate.
method Generalization of Loeffen et al. (2013) for a refracted Lévy process with a deterministic implementation delay.
result Compact and similar structure result for the probability of Parisian ruin.
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regul…
Study optimal stopping times for financial options with negative discount rates and random refraction times.
problem Optimal stopping times for financial options with negative discount rates and random refraction times.
method Analyzes optimal multiple stopping problems driven by Lévy processes with negative discount rates and random refraction times.
result Optimal strategy is uniquely characterized by up-crossing times, with thresholds determined explicitly or recursively.
Paper calculates the distribution of time spent below zero in risk models.
problem Analyzing time spent below zero in risk models.
method Analytical expressions for the distribution of occupation times.
result Improved understanding of risk processes by providing distribution formulas.
The paper optimizes utility for switching models using Lévy processes.
problem Maximizing HARA utilities in Lévy switching models.
method Dual method, f-divergence minimal martingale measures, Hellinger and Kulback-Leibler processes.
result Expressions for optimal strategies and maximal expected utilities.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LVY, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized field momentum obs…
Optimal dividend strategy found for risk models with regime switching.
problem Optimal dividend strategy for spectrally negative Markov additive models with regime switching.
method Introduced an auxiliary problem and transformed the original problem into a local optimization problem.
result The refraction-reflection strategy with regime-modulated thresholds is optimal.
In this paper we study a spectrally negative Lévy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with t…
Study on ruin probability with investment in risky assets modeled as semimartingales.
problem Analyzing ruin probability in a business process with investment in risky assets.
method Investigates ruin probability with investment in a Lévy process and semimartingale return, deriving upper bounds and conditions for ruin.
result Upper bounds on ruin probabilities decrease as a power function with increasing initial capital, and these bounds are asymptotically optimal.
Optimizes dividend policies in a Brownian model with controlled rates.
problem Realistic optimal dividend policies in a stochastic control problem.
method Delayed linear control strategies for refracted diffusion processes.
result Optimality of delayed linear control strategies for dividend payments.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
Optimal dividend strategies are found for companies with both continuous and lump sum payouts.
problem Determining the best dividend strategy for companies with both continuous and lump sum payouts.
method Using scale functions, explicit formulas for the expected present value of dividends until ruin are derived.
result A two-layer (a,b) strategy is shown to be optimal, paying continuous dividends above level a and lump sum payments above level b.
Study optimal stopping times for call-type payoffs in Levy processes using Canadization and phase-type fitting.
problem Optimal stopping times for call-type payoffs in spectrally negative Levy processes.
method Approximate refraction times with Erlang random variables and fit jumps to phase-type distributions. Use recursive algorithm to compute value function in closed form.
result Derive a recursive algorithm to compute the value function in closed form for optimal stopping times.
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
problem Solving inverse eigenvalue problems for symmetric potentials and refractive indices.
method Supervised regression models (k-Nearest Neighbours, Random Forests, Multi-Layer Perceptron) trained on eigenvalue datasets.
result Machine learning methods can numerically solve inverse eigenvalue problems under appropriate parameter tuning.
In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction period…
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…
Study optimal dividend strategy with capital injection for Lévy processes.
problem Optimal dividend strategy with capital injection under specific constraints.
method Used fluctuation identities of refracted-reflected Lévy process to derive explicit solution.
result Explicit optimal strategy and value function expressed in terms of scale function.
New model explains low interest rates and large bond market jumps.
problem Explaining recent observations in sovereign bond market.
method Introduces α-CIR model using α-stable Lévy process and branching property. result Unified and parsimonious model for low interest rates and large jumps.
New system studies trapped light paths in Euclidean space.
problem Trapping of light paths in Euclidean space with negative refractive index.
method Introduces wind-tree tiling billiards system to study trajectories of rays in Euclidean space with rectangular obstacles.
result Almost every configuration of the system traps trajectories with initial vertical direction in an infinite strip.
Constructs flows on quotients of Lie groups for Anosov subgroups.
problem Understanding dynamics on quotients of Lie groups by Anosov subgroups.
method Utilizes geometric structures and Lie group theory to construct and analyze flows.
result Establishes that all refraction flows arise from this construction.
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length δ, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
Characterizes flag geometries for Hitchin representations in SL3(R).
problem Understanding flag geometries associated with Hitchin representations in SL3(R).
method Geometric characterization based on invariant foliations and refraction flows.
result Constructs refraction flows for positive roots in general sl_n(R), with highest root flows being C^1+α.
Stability of PDEs linked to vector fields on manifolds.
problem Stability of solutions to differential equations involving vector fields.
method Analyzes Hyers-Ulam stability for global differential equations.
result Stability of solutions to the differential equation Vy=λy+f. The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virt…
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend poli…
An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.
In this paper we study the Omega risk model with surplus-dependent tax payments in a time-homogeneous diffusion setting. The new model incorporates practical features from both the Omega risk model(Albrecher and Gerber and Shiu (2011)) and the risk model with tax(Albrecher and Hipp (2007)). We explicitly characterize t…
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refraction explained by the existence of singularities in the Fresnel hyper-surface for Maxwell's equations on an anisotropic crystal.
Hamilton proved a theorem about focusing light rays, leading to new mathematical concepts.
problem Focusing light rays to a single point using optical instruments.
method Original proof and symplectic geometry proof of the Malus-Dupin theorem.
result A family of light rays can be focused to a single point if they are rectangular before entering the instrument.
Study on determining medium properties from wave travel times.
problem Determine anisotropic index of refraction from travel times.
method Geometry problems, boundary rigidity, lens rigidity, tensor tomography.
result Recent results on partial data in boundary and lens rigidity.
Generalizes Fermat's principle for wave propagation in cone structures.
problem Wave propagation in complex media with discontinuities and anisotropy.
method Generalizes Fermat's principle to smooth interfaces separating two cone structures representing wave propagation in various media.
result Conditions for critical points of arrival time functional, generalizing Snell's law and reflection.
Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model the occurrence of claims according to a Poisson process. The ruin is achieved wh…
The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
New method corrects complex distortions in single view images.
problem Complex distortions in images, especially those caused by refractive surfaces.
method Differentiable image sampling and semantic information augmentation.
result Model can estimate and correct highly complex distortions.
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously its coordinates as well as its momenta. The mathematical dscription of the phenome…
The study establishes conditions for stratified spaces to satisfy RCD(K, N) curvature-dimension condition.
problem Conditions for stratified spaces to satisfy RCD(K, N) curvature-dimension condition.
method Proves conditions for stratified spaces to satisfy RCD(K, N) using Ricci tensor bounds and cone angles.
result New examples of metric measure spaces satisfying RCD(K, N) curvature-dimension condition.
This paper sets baselines for reading comprehension benchmarks, finding simple models often perform well.
problem Understanding the difficulty of popular reading comprehension benchmarks.
method Established baselines for bAbI, SQuAD, CBT, CNN, and Who-did-What datasets.
result Simple models often outperform complex models on many benchmarks.
In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in non-uniform media. The corresponding equations of motion are also exposed, and som…
The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…
Material properties linked to Lie groupoids and algebroids in continuum mechanics.
problem Understanding material properties through groupoids and algebroids.
method Intuitive treatment of material groupoids and their algebroids.
result Material groupoids and algebroids are linked to material properties and their deformations.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…
Study negative discount rate effects on perpetual options in Lévy models.
problem Negative discount rate impacts perpetual American and Swing options in Lévy models.
method Analyze perpetual American and put options in exponential Lévy models with negative discount rate, identify critical continuation prices, and generalize to Swing type problems.
result Double continuation region arises in negative discount rate cases, identified by critical prices.
This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that travelt…
Modeling financial markets with a novel order flow model.
problem Inconsistent parameter values from long-range memory estimators.
method Tsallis q-exponential distribution for limit order cancellation times.
result Improved accuracy in predicting financial market dynamics.
Study proves projective Anosov subgroups lead to mixing flows in specific spaces.
problem Understanding mixing properties of flows on specific geometric spaces.
method Constructing non-empty domain of discontinuity in homogeneous space, using spectral estimates for transfer operators.
result Exponential mixing, spectral gap, and meromorphic continuation of zeta functions established.