This paper introduces a new method to price long-dated insurance contracts.
problem Pricing of long-dated, insurance-type contracts is complex and inconsistent.
method Loading pricing combines theoretically minimal and formally risk-neutral prices.
result Loading degree is constant for minimally fluctuating contracts and is a key characteristic.
Paper offers fast, accurate pricing for long-dated contracts using real-world probability measure.
problem Inaccurate pricing of long-dated contracts in insurance and pension funds.
method Applies RMQ and JRMQ algorithms under real-world measure, using benchmark approach.
result Prices are less expensive than risk-neutral valuation, highlighting departure from traditional methods.
We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility…
This paper investigates the pricing and hedging of variance swaps under a 3/2 volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the numéraire portfolio. The growth optimal portfolio is the numéraire portfolio and u…
Pricing extremely long-dated liabilities market consistently deals with the decline in liquidity of financial instruments on long maturities. The aim is to quantify the uncertainty of rates up to maturities of a century. We assume that the interest rates follow the affine mean-reverting Vasicek model. We model paramete…
We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence…
In this paper we show how to hedge a zero coupon bond with a smaller amount of initial capital than required by the classical risk neutral paradigm, whose (trivial) hedging strategy does not suggest to invest in the risky assets. Long dated zero coupon bonds we derive, invest first primarily in risky securities and whe…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the investor and the market value the options by risk-neutral expectations but under diffe…
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from conditional Asian options are determined only by average prices above certain t…
In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatil…
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.
We prove optimal mechanisms for general contract spaces.
problem Optimal mechanism design under adverse selection and ambiguity.
method Existence proof for optimal mechanisms in general contract spaces.
result Centralized contracting is equivalent to delegated contracting.
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.
Develops optimal currency hedging strategy for fund managers considering liquidity risk.
problem Choosing optimal foreign exchange (FX) hedge tenors to maximize carry returns within liquidity constraints.
method Time-dispersing total hedge value into future time buckets, maximizing FX carry benefit while adhering to liquidity risk metric (CFaR).
result Hedging strategy operates within liquidity budget, demonstrating practical insights for fund managers.
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.
Complexes' contractibility depends on the Collatz conjecture.
problem Determining contractibility of complex structures.
method Construction of complex structures and analysis of their contractibility.
result Contractibility of complex structures is linked to the Collatz conjecture.
Injectivity of fundamental group map proves contractibility of intersection in CAT(0) complexes.
problem Proving contractibility of intersections of subcomplexes in non-positively curved 2-complexes.
method Injectivity of the induced map from fundamental groups.
result Each component in the intersection of two contractible subcomplexes in a CAT(0) 2-complex is contractible.
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%.
The paper finds optimal insurance contracts in behavioral finance, avoiding moral hazard.
problem Finding optimal insurance contracts that avoid moral hazard in a behavioral finance framework.
method Formulated as a non-concave maximization problem involving Choquet expectation, then solved using calculus of variations.
result Optimal contracts are found for certain values of safety loading, with some contracts never optimal for others.
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…
Methodology projects forward electricity contract prices using market equilibrium and social welfare optimization.
problem Quantifying forward contract risks and optimizing revenue/cost for generators/load/traders.
method Market equilibrium and social welfare optimization; linear programming for total agents' welfare.
result Equilibrium contract price corresponds to the dual variable of equilibrium constraints.
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.
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.
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.
Regular languages describe contracting geodesics in groups.
problem Characterizing groups with infinite contracting geodesics.
method Analyzing geodesics in Cayley graphs with a contracting property.
result Groups with infinite contracting geodesics are either virtually Z or acylindrically hyperbolic.
Paper proposes machine learning for managing complex buyback contracts.
problem Managing complex buyback contracts, especially accelerated share repurchase.
method Proposes a machine learning method to optimally manage buyback contracts.
result Recovery of strategies similar to those obtained with partial differential equations and tree methods, but without the curse of dimensionality.
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…
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.
Proves measure contraction for specific sub-Riemannian structures.
problem Measure contraction properties in sub-Riemannian structures.
method Analytic sub-Riemannian structures and Lipschitz Carnot groups.
result Proves measure contraction properties for the structures.
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…
Groups can embed uniformly but not act properly on contractible manifolds.
problem Understanding the difference between group actions and embeddings on contractible manifolds.
method Analyzing the relationship between group actions and uniform embeddings on contractible manifolds.
result k-fold products of specific groups do not act on contractible manifolds.
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.
Corrects a false claim about a digital sphere model's contractibility.
problem Incorrect claim about MSS_18's 18-contractibility.
method Analyzes digital image MSS_18 as a digital model of S^2.
result Shows MSS_18 is 18-contractible.
Combines proportional and stop-loss reinsurance for insurer and reinsurer.
problem Addressing conflicting interests between insurer and reinsurer.
method Introduces proportional-stop-loss reinsurance using balanced loss function.
result Maximizes expected surplus for both insurer and reinsurer.
Algorithm learns optimal contracts for unaware principals.
problem Learning optimal contracts when principal is unaware of agent's utility and action space.
method Sequential contract offers with observed outcomes, using algorithm to approximate optimal contract.
result Algorithm learns optimal contract within epsilon of optimal net profit with bounded samples.
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.
Study on 4-manifolds splitting into contractible pieces.
problem Investigating contractible 4-manifolds that split into simpler pieces.
method Examining manifolds that decompose as Mn=A∪CB where A,B,C≈Rn or A,B,C≈Bn. result Exhibit large collections of 4-manifolds that split in the specified manner.
Surveying A1-homotopy theory and contractible varieties.
problem Understanding the relationship between A1-homotopy theory and contractible varieties. method Exploring the interplay between A1-homotopy theory and affine algebraic geometry. result Highlighting the connection between A1-homotopy theory and contractible varieties. 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.