Short proof shows only circles contract under curve shortening flow.
problem Characterizing contracting self-similar solutions of the curve shortening flow.
method Intuitive geometric proof using Gage's idea.
result Only circles contract under curve shortening flow.
Optimal contracts are found for agents with quadratic effort costs.
problem Finding optimal contracts in principal-agent problems with quadratic effort costs.
method Modeling the problem using Hamilton-Jacobi-Bellman (HJB) equations and proving the existence of classical solutions.
result Existence of optimal contracts for agents with quadratic effort costs is proven.
The paper shows how convex hypersurfaces contract under a specific curvature flow.
problem Understanding the behavior of convex hypersurfaces under curvature-driven contraction.
method Proves convergence of convex hypersurfaces in Rn+1 to a self-similar solution under a flow by powers of the Gauss curvature. result The limit of the flow is a smooth, uniformly convex self-similar solution, and under central symmetry, it is the round sphere.
Paper solves optimal contract problem for fund managers with capital injections and trading constraints.
problem Optimal contract for a fund manager with capital injections and endogenous trading constraints.
method Reduces the problem to an inverse problem of SPDE, proving well-posedness and computing the solution explicitly in the Black-Scholes model.
result Characterizes the solution to the inverse problem through a Stochastic Partial Differential Equation (SPDE).
We study the solution's existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract with contingent CSA. This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from z…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
problem Learning elliptic PDEs with noisy data and non-homogeneous boundary conditions.
method Bayesian approach with a Hölder space prior on neural network weights.
result Posterior contracts at near-minimax rate without prior knowledge of solution smoothness.
We prove that the only compact convex ancient solutions of the planar affine normal flow are contracting ellipses.
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.
Model clarifies network effects on CVA, revealing significant differences in derivative contract values.
problem Network effects on CVA in financial contracts.
method Developed a model to analyze default probabilities in a network of contracts.
result Network effects can significantly alter CVA values, leading to multi-modal distributions.
New mortgage contracts reduce underwater default by adjusting loan balances, but must balance prepayment incentives.
problem Underwater default incentives in mortgages.
method Analyzes automatic balance adjustment and prepayment penalties in mortgage contracts.
result Automatic balance adjustments are preferable to traditional contracts at certain spreads, reducing underwater default.
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownia…
Study develops precise solutions for complex economic models.
problem Constructing accurate solutions to dynamic equilibrium models on nonlocal domains.
method Uses the Contraction Mapping Theorem and Stable Manifold Theorem to derive approximate solutions.
result Proves convergence of approximate solutions to the true solution under certain conditions.
We study the contraction of a convex immersed plane curve with speed (1/α)k^{α}, where αin(0,1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. We also discuss a special symmetric case of type two blow-up and show that it converge…
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…
We prove that the only compact, origin-symmetric, strictly convex ancient solutions of the planar p centro-affine normal flows are contracting origin-centered ellipses.
We give a criterion under which a solution g(t) of the Kahler-Ricci flow contracts exceptional divisors on a compact manifold and can be uniquely continued on a new manifold. As t tends to the singular time T from each direction, we prove convergence of g(t) in the sense of Gromov-Hausdorff and smooth convergence away …
Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is…
AMM finds optimal contract for LPs to maximize order flow.
problem Maximizing order flow in AMMs with LPs.
method Leader-follower stochastic game, closed-form equilibrium solutions.
result LPs incentivized to add liquidity when external price attracts more noise trading.
Optimal contract found for risk averse agent and principal with unknown quality.
problem Finding an optimal contract for a risk averse agent and principal with unknown quality.
method Continuous time Principal-Agent model with exponential utility, moral hazard, and filtering of quality.
result Explicit solution to the optimal contract problem.
Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.
problem Preventing moral hazard in reinsurance contracts under non-concave premium principles.
method Develops optimal reinsurance contracts under a diffusion risk model with incentive compatibility constraints and extended distortion premium principles.
result An optimal reinsurance contract exists and is characterized by solving a double obstacle problem.
New MKABSDEs help calculate initial margins in financial contracts.
problem Calculating initial margins in financial contracts with dependencies.
method Introduced MKABSDEs, provided existence and uniqueness, applied to CVaR, used deterministic and Monte-Carlo methods for numerical approximations.
result MKABSDEs provide a new way to solve for initial margins in financial contracts.
We consider an ancient solution g(⋅,t) of the Ricci flow on a compact surface that exists for t∈(−∞,T) and becomes spherical at time t=T. We prove that the metric g(⋅,t) is either a family of contracting spheres, which is a type I ancient solution, or a Rosenau solution, which is a type II ancie…
Smart contracts are a digital technology with potential but also flaws.
problem Understanding the potential and limitations of smart contracts.
method Exploratory study combining statistics, IT, and law.
result Smart contracts have both idealistic promises and practical challenges.
Three theorems about arbitrage bubbles in financial equations.
problem Characterizing and solving generalized Black-Scholes equations with arbitrage bubbles.
method Analytical proofs of three theorems using the Feynman-Kac theorem.
result Exact solutions for Call contracts with arbitrage bubbles.
Study optimal reinsurance for insurers with a reinsurer's default risk.
problem Optimal reinsurance for insurers with a reinsurer's default risk.
method Analytical solution for two types of reinsurance contracts.
result Joint effect of reinsurer's default and background risk on reinsurance demand.
Insurance speeds wealth growth by altering wealth dynamics.
problem Why do people voluntarily take insurance when it increases wealth inequality?
method We evaluated contracts by their effect on the time-average growth rate of wealth, assuming only knowledge of wealth dynamics.
result The puzzle of voluntary insurance contracts disappears when wealth changes are non-ergodic.
This paper improves insurance contracts by ensuring increasing indemnities and retention functions.
problem Moral hazard in insurance contracts for smaller losses.
method Characterizing optimal solutions via calculus of variations and applying to specific criteria.
result Explicitly expressed contracts for problems with Yaari's dual criterion and general RDU.
This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fi…
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
3-manifolds with positive scalar curvature and bounded geometry are contractible.
problem Characterizing 3-manifolds with positive scalar curvature and bounded geometry.
method Maximal weak solution to inverse mean curvature flow.
result Complete contractible 3-manifolds with positive scalar curvature and bounded geometry are R3. Optimizes long-term portfolios considering non-uniformly ergodic economic factors.
problem Optimizing long-term portfolios with non-uniformly ergodic economic factors.
method Solves Bellman equation using local span contraction with weighted norms.
result Form of optimal strategy presented.
New bounds for SA with arbitrary norm contractions and Markovian noise.
problem Finite-time analysis of two-time-scale stochastic approximation with arbitrary norm contractions and Markovian noise.
method Use of generalized Moreau envelope for arbitrary norm contractions and solutions of Poisson equation for Markovian noise.
result Mean square error decays at rates of O(1/n2/3) and O(1/n) under different conditions. We consider an embedded convex ancient solution Γt to the curve shortening flow in R2. We prove that there are only two possibilities: the family Γt is either the family of contracting circles, which is a type I ancient solution, or the family of evolving Angenent ovals, which correspond to a type II …
We consider two types of p-centro affine flows on smooth, centrally symmetric, closed convex planar curves, p-contracting, respectively, p-expanding. Here p is an arbitrary real number greater than 1. We show that, under any p-contracting flow, the evolving curves shrink to a point in finite time and the only…
New smooth solutions of the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton based on the quaternionic Heisenberg group are constructed. We show that through appropriate contractions the solutions found in the G2-heterotic case converge to the heterotic solutions on 6-dimensi…
Adaptive pricing framework for perpetual contracts using liquidity curves and oracles.
problem Ensuring stable and predictable pricing for perpetual contracts.
method Uses liquidity curves and on-chain oracles with parabolic and sigmoid functions to quote prices and fees.
result Ensures pricing stability and predictability through adaptive pricing framework.
This paper optimizes reinsurance contracts with belief differences between insurer and reinsurer.
problem Dynamic reinsurance design with heterogeneous beliefs under mean-variance framework.
method Modeling surplus process, applying partitioned domain optimization, solving HJB system.
result Optimal reinsurance contracts with belief heterogeneity are more complex than standard contracts.
Model optimizes mediation for insolvent suppliers by finding an optimal contract solution.
problem Optimizing contract outcomes for insolvent suppliers in disputes.
method Linear optimization model with complex number phasor approach and Gompertz function for supplier offers.
result Optimal solution adherence to initial contract terms.
The present work studies and analyzes general defaultable OTC contract in presence of a contingent CSA, which is a theoretical counterparty risk mitigation mechanism of switching type that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever sh…
The paper calculates fair strike for variance swaps on time-changed Markov processes.
problem Calculating fair strike for variance swaps on time-changed Markov processes.
method Proving the fair strike equals the price of a European contract and solving the integro-differential equation.
result The fair strike for variance swaps can be computed explicitly for certain Markov processes.
The paper uses neural networks to price complex life insurance contracts with multiple risk factors.
problem Pricing equity-linked life insurance contracts with various stochastic risk factors.
method Assuming hedging to reduce local variance, the price is expressed as a system of non-linear PDEs. Reformulated as a backward SDE with jumps, solved numerically using neural networks.
result Neural networks provide an efficient numerical solution for pricing these complex contracts.
This paper considers a mortgage contract where the borrower pays a fixed mortgage rate and has the choice of making prepayment. Assume the market interest follows the CIR model, a free boundary problem is formulated. Here we focus on the infinite horizon problem. Using variational method, we obtain an analytical soluti…
Optimal trading strategy for multiple futures contracts with stochastic bases.
problem Dynamic trading of multiple futures contracts with different underlying assets.
method Proposed a multi-dimensional scaled Brownian bridge model to capture joint dynamics, leading to semi-explicit solutions of HJB equations.
result Derived optimal long-short trading strategy that considers contango and backwardation.
Generative model improves tabular data density estimation.
problem Challenges in estimating tabular data distribution.
method Tensor contraction layers and transformers in VAEs.
result Embedding representations improve density estimation metrics.
Optimal strategies identified for unit linked life insurance contracts in a jump-diffusion model.
problem Mean-variance hedging of unit linked life insurance contracts with basis risk.
method Time-consistent mean-variance portfolio selection problem solved with Nash subgame perfect equilibrium and PIDEs.
result Explicit solution to the extended HJB system and optimal trading strategies in closed-form.
Study optimal contracts for Principals hiring a common Agent in continuous time.
problem Optimal contracts for Principals hiring a common Agent in a continuous time setting.
method Reduction of optimisation problem to coupled HJB equations, analysis of specific linear-quadratic model.
result Optimal effort and remunerations coincide only in the first best case.
Paper offers a new method to solve risk-sharing problems in Principal-Agent models.
problem Risk-sharing in Principal-Agent models with CARA utilities.
method Optimal decomposition of expected utility using Reverse-H{ö}lder inequality.
result Proof of existence and uniqueness of the solution under general assumptions.