In earlier work we introduced topologically minimal surfaces as the analogue of geometrically minimal surfaces. Here we strengthen the analogy by showing that complicated amalgamations act as barriers to low genus, topologically minimal surfaces.
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48 results for “geometric barriers”
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order .
The paper prices long-term options with a reflecting barrier model.
problem Pricing long-term options with asset price limits.
method Model asset price as geometric Brownian motion with a lower reflecting barrier, pricing options using compound options.
result Option prices can be determined using standard risk-neutral arguments, and hedging strategies are available.
Study geometric step options with jumps, deriving pricing equations and characterizations.
problem Pricing geometric step options in markets with jumps.
method Symmetry and parity relations, partial integro-differential equations, ordinary integro-differential equations.
result Derive semi-analytical pricing results for geometric step options.
We show the existence of a deformation process of hypersurfaces from a product space into another product space such that the relation of the principal curvatures of the deformed hypersurfaces can be controlled in terms of the sectional curvatures or Ricci curvatures of and . In t…
On the surplus management of funds with assets and liabilities in presence of solvency requirementsmath.OC
The paper optimizes dividend strategies for companies with assets and liabilities under solvency constraints.
problem Maximizing dividends while adhering to solvency requirements in the face of correlated asset and liability movements.
method Developed verification lemmas to show optimal barrier dividend strategies in two cases: with and without shareholder funding.
result Optimal dividend strategies are barrier-type, derived in closed form and illustrated.
We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider the op…
Alternative solvability criterion for minimal surface equations and mean curvature flow.
problem Solvability of Dirichlet problem for minimal surface equation in non-mean convex domains.
method Introduces a structural condition from a second-order ODE to construct boundary barriers, applicable to unbounded domains and Hadamard manifolds.
result Allows solvability under geometric hypotheses different from classical Jenkins-Serrin theory, applicable to Euclidean space and mean curvature flow.
Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.
problem Understanding the dynamics and geometric barriers in tubular origami structures.
method Kolmogorov--Arnold--Moser (KAM) theory and numerical simulations.
result Invariant curves persist in large module limits, providing phase-space interpretation of folding modes.
Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.
problem Analyzing ancient caloric functions on manifolds beyond volume doubling.
method Time polynomial structure result on ancient caloric functions with polynomial growth.
result Finiteness result for ancient caloric functions is essentially sharp, except for multi-end cases.
The paper calculates prices for multi-step barrier options under the Black-Scholes model.
problem Calculating prices for multi-step barrier options with varying barriers and time steps.
method Derives a general, explicit expression for option prices using the Black-Scholes model and a multi-step reflection principle.
result Derives a multi-step reflection principle that generalizes the reflection principle of Brownian motion.
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
A new method uses deep learning to price barrier options.
problem Pricing barrier options with boundary conditions.
method Forward deep BSDEs with added nodes for barrier conditions.
result Can handle any barrier condition and boundary conditions.
We consider the teacher-student setting of learning shallow neural networks with quadratic activations and planted weight matrix , where is the width of the hidden layer and is the data dimension. We study the optimization landscape associated with the empirical and the popula…
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose …
A time-dependent double-barrier option is a derivative security that delivers the terminal value at expiry if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval . Using a probabilistic approach we obtain a decomposition of the barrier opti…
We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing metho…
Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hitq-fin.CP
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
In this paper, we are concerned with hypersurfaces in with constant r-mean curvature, to be called -hypersurfaces. We construct examples of complete -hypersurfaces which are invariant by parabolic screw motion or by rotation. We prove that there is a unique rotational strictly convex entire $H_r…
Hamiltonian method applied to floating barrier options pricing.
problem Pricing of floating barrier options.
method Hamiltonian approach in quantum mechanics applied to barrier options.
result Analytical expressions for pricing kernel and option price derived.
Deep learning solves barrier options with stochastic volatility.
problem Solving barrier options with stochastic volatility.
method Unsupervised deep learning neural networks trained to satisfy PDE and boundary conditions.
result Neural networks accurately price barrier options in a single framework.
New method tackles bilevel optimization with polyhedral constraints.
problem Challenges in bilevel optimization with active-set changes and expensive Hessian inversions.
method Logarithmic barrier smoothing and proxy-gradient algorithm for differentiable approximation.
result Stationarity rates of in deterministic setting and under stochastic noise.
Unified pricing method for FX options with barriers.
problem Calculating the value and sensitivities of FX options with barriers.
method Unified Vanna-Volga pricing technique for single and double barrier FX options.
result Derivation of closed formulas for Delta, Vega, Vanna, and Volga.
Root's barrier is continuous and finite under certain conditions.
problem Continuity of the root barrier function.
method Analyzing Skorokhod embedding problem and properties of target measures.
result The barrier function is continuous and finite under specified conditions.
Interior-point methods adapted for manifolds, achieving similar optimization results.
problem Optimizing on manifolds with self-concordant barriers.
method Generalization of self-concordance to Riemannian manifolds, path-following method analysis.
result Local quadratic convergence of Newton's method and standard complexity guarantees.
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricingq-fin.PR
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or disc…
Research provides explicit NPV expressions for double barrier strategies.
problem Calculating expected NPVs of double barrier strategies for regular diffusions.
method Explicit expression using bivariate q-scale function with perturbation technique.
result Explicit expressions for expected NPVs are derived for certain cases.
New symplectic barriers found in ball embeddings.
problem Existence of symplectic embeddings with intersections.
method Proving obligatory intersections with symplectic planes.
result Existence of symplectic barriers in ball embeddings.
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show that the proposed method always outperforms the standard Monte Carlo approach an…
We consider the mean curvature flow of compact convex surfaces in Euclidean -space with free boundary lying on an arbitrary convex barrier surface with bounded geometry. When the initial surface is sufficiently convex, depending only on the geometry of the barrier, the flow contracts the surface to a point in finite…
Barrier Option Pricingmath.AP
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not smooth. However, for barrier options, this restriction can be accommodated and a sy…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular atten…
Geometric analysis proves weak KAM solutions constant under specific conditions.
problem Conditions for weak KAM solutions to be constant.
method Geometric and differential analysis of Hamilton-Jacobi equations.
result Weak KAM solutions are constant if and only if the 1-form is harmonic.
We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4-space with barrier 3-spheres. \par The existe…
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted …
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…
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a comparison principle with geometric barriers for establishing mean curvature estimates fo…
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
Study short-term behavior of up-and-in barrier options using Malliavin calculus.
problem Analyzing the decay rate of up-and-in barrier option prices as maturity decreases.
method Use Malliavin calculus to analyze the law of the supremum of the log-price process.
result Derive upper bound on asymptotic decay rate of up-and-in barrier option prices.
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, w…
Paper formalizes multi-dimensional FSD using geometric methods.
problem Complex measure theory and calculus barriers to formalization in proof assistants.
method Geometric framework for first-order stochastic dominance in N dimensions.
result Geometric approach bypasses complex integration theory for direct comparison of survival probabilities.
We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.
Study efficient pricing for barrier options in stochastic-volatility models with leverage correction.
problem Barrier options are sensitive to volatility dynamics, especially leverage, making accurate pricing difficult.
method Developed a class of continuous-path stochastic-clock volatility models and a systematic small-ρ expansion to incorporate leverage.
result Transform-only pricing formulas for barrier derivatives are fast and numerically stable, even for negative leverage.
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the opponent (stochastic, adversarial, or intermediate), the order of the players' mo…