The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.
Computable contracts simplify financial transactions and reduce legal costs.
problem Difficulty in querying, executing, and analyzing text-based financial contracts.
method Develop a Contract Definition Language and illustrate use cases.
result Substantial improvements in customer experience and cost reduction.
In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any c…
Optimal execution strategy for merger & acquisition contracts with price impact.
problem Optimal execution and pricing of financial derivatives in M&A deals.
method Indifference utility arguments, considering linear and nonlinear contracts.
result Linear contracts are more expensive and vulnerable to manipulation.
This paper develops a method to select a reference contract for multi-contract quoting to minimize execution risk.
problem Minimizing execution risk in multi-contract quoting sequences.
method Develops a diagnostic framework using order-flow Hawkes forecasts and CLF to select a stable reference contract.
result Event-history and LOB-state signals offer complementary views for reference-contract selection.
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.
We consider a general framework of optimal mechanism design under adverse selection and ambiguity about the type distribution of agents. We prove the existence of optimal mechanisms under minimal assumptions on the contract space and prove that centralized contracting implemented via mechanisms is equivalent to delegat…
Improved security of smart contracts by classifying them into four categories.
problem Detecting and classifying vulnerabilities in smart contracts efficiently.
method Used AWD-LSTM for multi-class classification, addressing class imbalance.
result Achieved a weighted average Fbeta score of 90.0%.
Study on contracting maps and their rigidity under curvature constraints.
problem Rigidity of contracting maps between manifolds with positive curvature.
method Analysis of curvature pinching and contracting conditions involving singular values.
result Established the relation between curvature pinching and contracting conditions.
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…
Study shows some contractible complexes can't have certain immersions.
problem Understanding non-positive immersions in contractible complexes.
method Provided counterexamples to a conjecture by Wise.
result Some contractible complexes do not have non-positive immersions.
This paper presents some partial answers to the following question. QUESTION. If a normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, must X be contractible? The main results of the paper are: THEOREM 1. If a normal space X is the union…
The simplicial volume of non-R^3 contractible 3-manifolds is infinite.
problem Characterizing contractible 3-manifolds based on their simplicial volume.
method Analyzing the simplicial volume of contractible 3-manifolds and open 3-manifolds.
result The Euclidean space is the unique contractible 3-manifold with vanishing minimal volume.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
Optimal contracts help principals delegate data collection in decentralized ML.
problem Dealing with information asymmetries in decentralized ML.
method Design of optimal and near-optimal contracts addressing uncertainty in model quality and performance.
result Simple linear contracts achieve 1-1/e fraction of optimal utility.
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.
Fair insurance contracts are designed to handle default risk using cooperative game theory.
problem Designing fair insurance contracts in the presence of default risk.
method Cooperative game theory to specify premiums and participation in benefit.
result Fair benefit participation emerges as a game outcome involving residual risks.
One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytop…
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 …
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.
We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, rank one isometries in groups acting properly on proper CAT(0) spaces, elements acting hyperbolically on the Bass-Serr…
Paper presents LLM-enhanced contract metadata extraction.
problem Automatic detection and annotation of legal clauses in contracts.
method Integration of publicly available and proprietary datasets with advanced LLM methodologies.
result Substantial improvements in clause identification accuracy and efficiency.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
Let X be a contractible 2-complex which is a union of two contractible subcomplexes Y and Z. Is the intersection Y∩Z contractible as well? In this note, we prove that the inclusion-induced map π1(Y∩Z)→π1(Z) is injective if Y is π1-injective subcomplex in a locally CAT(0) 2-co…
Proves equivalence of two types of boundaries in metric spaces.
problem Proving equivalence of two types of boundaries in metric spaces.
method Analyzes and compares contracting and κ-Morse boundaries. result Proves equivalence of 1-Morse boundary and contracting boundary as topological spaces.
This work presents a methodology for forward electricity contract price projection based on market equilibrium and social welfare optimization. In the methodology supply and demand for forward contracts are produced in such a way that each agent (generator/load/trader) optimizes a risk adjusted expected value of its re…
New proof for hyperbolic groups using contracting boundaries of cusped spaces.
problem Proving groups are hyperbolic relative to subgroups.
method Proving compact contracting boundary of cusped space implies hyperbolicity.
result If cusped space Gh has compact contracting boundary, then G is hyperbolic relative to subgroups H. Curvature conditions distinguish Euclidean space and disks in contractible manifolds.
problem Distinguish Euclidean space and disks among contractible manifolds.
method Investigate curvature conditions on open and compact contractible manifolds with boundary.
result Stronger curvature conditions can distinguish disks from Euclidean spaces.
A reinsurance contract should address the conflicting interests of the insurer and reinsurer. Most of existing optimal reinsurance contracts only considers the interests of one party. This article combines the proportional and stop-loss reinsurance contracts and introduces a new reinsurance contract called proportional…
Prediction markets can be manipulated by traders who can move contract settlements, harming price discovery.
problem Manipulation of settlement times in prediction markets leads to unfair wealth transfer and harms price discovery.
method Developed a model showing how settlement manipulation transfers wealth and harms price discovery, and observed real-world effects on Polymarket's Bitcoin contract.
result Manipulators capture significant profits from retail traders, especially when settlement times are short.
Predicts short-term futures contract direction using neural networks and order flow data.
problem Challenges in predicting short-term directional movement of futures contracts.
method Engineering features from technical analysis, order flow, and order-book data; training a Tabnet neural network.
result Achieved an accuracy of 0.601 in predicting directional change on the Silver Futures Contract.
Paper provides a method to price electricity storage contracts using COS technique.
problem Valuation of electricity storage contracts considering physical and operational constraints.
method Uses Fourier-based COS method to price contracts based on stochastic polynomial process.
result The COS method accurately and efficiently prices electricity storage contracts.
LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.
problem Analyzing trade-offs between privacy and utility in estimation problems.
method Equivalence of LDP constraints to contraction coefficients of E_γ-divergence, using f-divergences and estimation-theoretic tools.
result LDP guarantees can be expressed in terms of contraction coefficients of arbitrary f-divergences.
The paper analyzes game theory in convertible contracts during liquidity events.
problem Optimizing payments in convertible contracts during liquidity events.
method Defined a general model for games, showed non-existence of pure strategy Nash equilibria, developed algorithms for computing equilibria.
result Optimum pure strategy Nash equilibria exist when all contracts are of the same type (SAFE).
Exotic diffeomorphism survives stabilizations on a contractible 4-manifold.
problem Finding exotic diffeomorphisms on contractible 4-manifolds.
method Developed a Pin(2) × Z_2-equivariant refinement for computing Seiberg-Witten Floer homotopy types.
result Constructed an exotic diffeomorphism that survives two stabilizations.
Let X be a proper CAT(0) space and let G be a cocompact group of isometries of X which acts properly discontinuously. Charney and Sultan constructed a quasi-isometry invariant boundary for proper CAT(0) spaces which they called the contracting boundary. The contracting boundary imitates the Gromov boundary for $δ…
We prove that a contractible orbifold is a manifold.
Compact Kähler manifolds with positive curvature have contractible covers.
problem Compact Kähler manifolds with positive sectional curvature.
method Proves contractibility of universal cover.
result The universal covering of a compact Kähler manifold with small positive sectional curvature is contractible.
We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.
A contraction analysis improves model-based RL's error recovery.
problem Theoretical understanding of model-based reinforcement learning.
method Contraction analysis applied to both stochastic and deterministic state transitions.
result Error reduction in cumulative reward using branched rollouts.
Develops a contraction framework for MCMC mixing rates.
problem Proving mixing-time bounds for MCMC algorithms.
method Global and local contraction coefficients under Eγ-divergence. result Explicit global contraction coefficients for Gaussian smoothing.
In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric Lévy process. We consider four contracts, three of which were introduced in Zhang et al. (2013) for a geometric Brownian motion. The first one is an i…
Quantum channels' contraction under privacy constraints studied.
problem Understanding the privacy constraints on quantum channel contractions.
method Established upper bounds on contraction coefficients for specific divergences under QLDP constraints.
result Upper bounds and full characterization of contraction coefficients for specific quantum distances.
Formula found for skinning map contraction in hyperbolic geometry.
problem Finding the contraction constant of skinning maps.
method Elementary hyperbolic geometry and moduli spaces of hyperbolic manifolds.
result Explicit formula for contraction constant.
The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
Ethereum smart contracts have recently drawn a considerable amount of attention from the media, the financial industry and academia. With the increase in popularity, malicious users found new opportunities to profit by deceiving newcomers. Consequently, attackers started luring other attackers into contracts that seem …
Random walks on metric spaces embed quasi-isometrically into the space.
problem Embedding random subgroups of metric spaces quasi-isometrically.
method Analyzing random walks and contracting elements in metric spaces.
result Random subgroups of isometry groups are quasi-isometrically embedded.
Study loan contracts in DLPs using derivatives pricing and neural networks.
problem Optimizing and hedging risks in decentralized lending contracts.
method Derivatives pricing theory, deep neural networks, and statistical arbitrage.
result Developed a method to hedge risks in lending contracts and exploit arbitrage opportunities.