Probabilistic analysis reveals substantial losses for reverse convertible note holders.
problem Substantial losses to reverse convertible note holders due to complex pricing.
method Probabilistic analysis using Law of Total Expectation.
result Note-holders likely suffered substantial losses under various market scenarios.
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…
Classifies orientation-reversing homeomorphisms of even periods on surfaces.
problem Classifying orientation-reversing homeomorphisms of even periods on surfaces.
method Following the approach of [1] and correcting errors in [1] for the case of periods multiple of 4.
result Classification for orientation-reversing homeomorphisms of periods multiple of 4.
A quandle orbit's orientation is problematic when reversed.
problem The natural orientation-reversal of quandle orbits is unsuitable for medial quandles.
method Defined the orientation-reversal of a quandle orbit by inverting translations, observed it's unsuitable for medial quandles.
result The natural orientation-reversal of quandle orbits is unsuitable for medial quandles.
A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodes…
Author corrects an error in a paper about certain knot surgeries.
problem Correcting an error in a paper about knot surgeries.
method Analyzing and reporting an error in a previous paper.
result An error in a previous paper about knot surgeries has been identified and corrected.
The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression ->…
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
The operation of (untwisted) Whitehead doubling trivializes the Alexander module of a knot (and consequently, all known abelian invariants), and converts knots to topologically slice ones. In this note we show that Whitehead doubling does not trivialize the rational function that equals to the 2-loop part of the Kontse…
This note clarifies connections between Föllmer process and DDPM sampler.
problem Understanding the relationship between Föllmer process and DDPM sampler.
method Direct discretization of the Föllmer process and DDPM sampler analysis.
result Discretized Föllmer processes provide optimal hyper-parameters for DDPM samplers.
A method for converting NIW parameters for better estimation.
problem Estimating parameters of multivariate normal distribution.
method Convergent procedure for converting mean parameters to natural parameters in NIW family.
result Maximum likelihood estimation of natural parameters from observed statistics.
Deep learning converts one singer's voice to another without supervision.
problem Unsupervised singing voice conversion.
method Deep learning network with a single CNN encoder, WaveNet decoder, and classifier.
result Natural, recognizable singing voices converted without supervision.
New measure quantifies function similarity for optimization.
problem Measuring similarity between functions for optimization.
method Quantifies sub-optimality gaps and operation rules.
result Unified measure for various functional similarities.
Study finds actuarial unfairness in China's pension system, proposing income-dependent annuitization rules.
problem Actuarial fairness in China's NDC pension system when mortality differs across income groups.
method Developed a mortality-differentiated Lee-Carter framework with group-specific baseline mortality schedules and a common period effect, estimated using national and subgroup data.
result Substantial actuarial unfairness in the current age-only divisor, with a reverse transfer from poorer to richer retirees.
In the present paper we show that the Binomial-tree approach for pricing, hedging, and risk assessment of Convertible bonds in the framework of the Tsiveriotis-Fernandes model has serious drawbacks. Key words: Convertible bonds, Binomial tree, Tsiveriotis-Fernandes model, Convertible bond pricing, Convertible bond Gree…
Structured products led to severe losses, revealing flaws in investor protection.
problem Flaws in structured investment products causing investor losses.
method Probabilistic analysis using the Law of Total Expectation.
result Investors were likely to experience grave difficulties from the start.
Efficient method for pricing European and American options using Markov switching stochastic volatility model.
problem Modeling and pricing options under varying volatility and mean-reversion speeds.
method Discrete-time Markov switching stochastic volatility with co-jump model, computationally efficient approach for European options, and conversion to European option pricing for American options.
result Efficient and accurate methods for pricing options, including variance swap analysis.
Deep learning models price convertible bonds with complex reset and call features.
problem Pricing convertible bonds with path-dependent reset and call provisions.
method Formulated as a PPDE, deep learning approximates conditional expectations.
result Deep learning produces stable and accurate prices across various model specifications.
Removes all bad local minima without adding extra units.
problem Neural network loss landscapes have bad local minima.
method Converts all bad local minima to non-local minima at infinity using auxiliary parameters.
result Removes all bad local minima from any loss landscape.
Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.
problem Analyze the convergence of diffusion-based generative models under minimal assumptions.
method Model the generation process as a composition of reverse ODE and noising steps, leveraging Wasserstein-type error control and noise addition.
result Achieved a linear dependence on data dimension and improved dependence on discretization step size for KL divergence error.
Study callable convertible bonds with liquidity constraints, generalizing previous work.
problem Callable convertible bond problem with liquidity constraints.
method Introduced a new technique to handle non-ordered payoff situations.
result Complete solution to callable convertible bond problem with liquidity constraint.
In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) short-rate is not deterministic. When the band is narrow, we ca…
This paper converts speech to match a face image and vice versa.
problem Matching speech to a face image and vice versa.
method Proposes a model with speech converter, face encoder/decoder, and voice encoder.
result Trained model converts speech to match a face image and generates a face image that matches the voice of input speech.
Classifies reversible and strongly reversible elements in quaternionic groups.
problem Classifying reversible and strongly reversible elements in quaternionic groups.
method Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
result Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.
problem Classifying reversible and strongly reversible elements in Hermitian isometry groups.
method Classification through group theory and algebraic manipulation.
result New classification of strongly reversible elements in Sp(n).
The paper classifies reversible and strongly reversible elements in quaternionic hyperbolic spaces.
problem Classifying reversible and strongly reversible elements in quaternionic hyperbolic spaces.
method Analyzing conjugacy classes and using properties of quaternionic hyperbolic spaces and their isometry groups.
result All elements of the isometry group of quaternionic hyperbolic spaces are strongly reversible.
An end sum is a non-compact analogue of a connected sum. Suppose we are given two connected, oriented n-manifolds M1 and M2. Recall that to form their connected sum one chooses an n-ball in each Mi, removes its interior, and then glues together the two Sn−1 boundary components thus created by an orien…
The paper examines how CoCo bonds can enhance financial stability in interconnected banking systems.
problem Enhancing financial stability in interconnected banking systems.
method Financial network model with contingent convertible (CoCo) debt obligations.
result Replacing unsecured interbank debt with CoCo debt decreases systemic risk and increases bank shareholder value.
This paper classifies reversible and strongly reversible elements in affine groups.
problem Classifying reversible and strongly reversible elements in affine groups.
method Identifying affine transformations and using conjugacy by involutions.
result Classification of reversible and strongly reversible elements in affine groups.
The paper validates a classifier for identifying intraday regime shifts in MNQ futures.
problem Developing reliable trading signals from intraday regime shifts in MNQ futures.
method Constructed a composite day-classification system using three observable conditions.
result Classifier-positive days exhibit distinct intraday behavior but fail to generate profitable trading signals.
Study finds mean reversion strategies perform well on historical data but fail in recent market conditions.
problem Performance of mean reversion strategies in recent market data.
method Empirical investigation of three mean reversion strategies (PAMR, OLMAR, TCO) on historical S&P 500 data and benchmark datasets.
result Mean reversion strategies may fail in recent market conditions, especially with transaction costs.
Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.
problem Understanding cubic graphs and their relation to bridge trisections.
method Proving every Tait-colored cubic graph is a 1-skeleton of a bridge trisection.
result Every Tait-colored cubic graph corresponds to a bridge trisection of a knotted surface.
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).
New neural net learns time-reversible symplectic dynamics.
problem Lack of time-reversibility in neural networks for symplectic systems.
method Proposes a new neural network architecture for time-reversible symplectic systems.
result Demonstrates learning of time-reversible symplectic dynamics from data.
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
Algebraic method reveals criterion for quaternionic Möbius group reversibility.
problem Characterizing reversibility in quaternionic Möbius group elements.
method Purely algebraic approach using matrix entries and conjugacy invariants.
result Explicit criterion for reversibility in terms of matrix entries.
New method makes robust estimators work without knowing corruption levels.
problem Robust estimation algorithms struggle with unknown corruption levels.
method Abstracted geometric puzzle solution to universal meta technique.
result Converts any robust estimator to work without corruption bounds.
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
Sharp stability results for reverse isoperimetric inequalities in 2D.
problem Reverse isoperimetric inequalities in the plane.
method Stability analysis of λ-convex bodies and convex bodies with smooth boundaries. result Sharp stability results for reverse isoperimetric inequalities, including inradius and Cheeger inequalities.
Modeling cryptocurrency spot-quotient variation as a diffusion process.
problem Intraday variation between ETHBTC spot and quotients on Binance.
method Modeling variation as an Ornstein-Uhlenbeck process, testing for mean-reversion, using maximum likelihood estimation.
result Intraday variation is not constant at 0, showing mean-reversion behavior with larger deviations in the first year.
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
Boundary rigidity proven for non-reversible Finsler metrics.
problem Recovering non-reversible Finsler metrics from boundary distance data.
method Sum of reversible Finsler norm and closed 1-form, boundary rigidity results.
result 1-form can be uniquely recovered from boundary distance data.
Book provides detailed trading strategies for various asset classes.
problem None explicitly stated, but addresses the need for trading strategies.
method Detailed descriptions and mathematical formulas for over 150 trading strategies.
result Provides comprehensive strategies for multiple asset classes.
New method neutralizes gender bias in word embeddings without losing semantic information.
problem Gender biases in word embeddings trained on human-generated corpora.
method Latent Disentanglement and Counterfactual Generation with siamese auto-encoder and gradient reversal layer.
result Our method outperforms existing debiasing methods in preserving semantic information and neutralizing gender biases.
Convolutional network converts speaker voices without text.
problem Speaker conversion without text-based methods.
method Fully convolutional wav-to-wav network with ASR pre-training.
result Successfully converts TTS robot's voice to narrated audiobook voices.
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
New theory improves diffusion model convergence for generating data.
problem Improving convergence of diffusion models for data generation.
method Developed a non-asymptotic convergence theory for probability flow ODEs.
result Proves d/ε iterations suffice for approximating target distributions. New Dynkin games with Poisson intervention times studied for convertible bond strategies.
problem Optimal stopping strategies for convertible bonds with random intervention times.
method Characterized by backward stochastic differential equations.
result Optimal conversion and calling strategies for convertible bonds derived.