Investigates good deal bounds for financial markets with convex constraints.
problem Financial market models with convex constraints.
method Study of good deal valuation as a convex risk measure.
result Properties of good deal valuation and its relation to superhedging cost and FTA.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on …
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Study good-deal hedging under uncertain market prices, reducing speculative components.
problem Good-deal valuation under model uncertainty and speculative risk.
method Robust approach using backward stochastic differential equations.
result Reduction or elimination of speculative components in good-deal hedging.
Study robust hedging and valuation under combined uncertainty about asset price drifts and volatilities.
problem Robust hedging and valuation under uncertainty about asset price drifts and volatilities.
method Non-dominated multiple priors approach to model uncertainty, worst-case good-deal bounds, coherent risk measures, second-order backward stochastic differential equations.
result Characterization of hedging strategies and good-deal bounds via solutions to backward stochastic differential equations.
We consider option pricing in a regime-switching diffusion market. As the market is incomplete, there is no unique price for a derivative. We apply the good-deal pricing bounds idea to obtain ranges for the price of a derivative. As an illustration, we calculate the good-deal pricing bounds for a European call option a…
In an L∞-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…
Study financial contracts pricing in markets with nonproportional costs and constraints.
problem Financial contract pricing in markets with nonproportional transaction costs and portfolio constraints.
method Direct and dual characterization of market-consistent prices with acceptable risk thresholds.
result Extension of the Fundamental Theorem of Asset Pricing to include good deals and scalable good deals.
This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with …
A new metric uses nonparametric comparison for fitting parametric distributions.
problem Measuring goodness-of-fit for nonlinear models using maximum likelihood estimation.
method Survival Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) for nonparametric comparison. result The ESJS can be used as a measure of goodness-of-fit in maximum likelihood estimation. We explore in some detail the notion of algorithmic stability as a viable framework for analyzing the generalization error of learning algorithms. We introduce the new notion of training stability of a learning algorithm and show that, in a general setting, it is sufficient for good bounds on generalization error. In t…
Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…
The paper analyzes set-to-set matching with neural networks, focusing on theoretical generalization.
problem Theoretical analysis of set-to-set matching with neural networks.
method Generalization error analysis of set-to-set matching with neural networks.
result Theoretical insights into the behavior of set-to-set matching models.
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph cluste…
The paper introduces a new method to find meaningful data subsets in multivariate probability density functions.
problem Finding meaningful data subsets in multivariate probability density functions.
method The paper defines an abstract bump construct based on curvature functionals of the probability density and proposes a multivariate implementation of Good and Gaskins' original concave bumps.
result The method provides theoretical results for asymptotic consistency of bump boundaries and confidence regions.
MCN improves deep neural networks by bettering local minima and generalizing well.
problem Bad local minima and poor generalization in deep neural networks.
method Introducing Maximum-and-Concatenation Networks (MCN) to eliminate bad local minima and improve generalization.
result MCN can autonomously improve local minima's goodness by increasing network depth.
Proposes a method to handle input uncertainties in regression trees.
problem Uncertainties in input variables in regression problems.
method Adapting standard regression trees to account for input uncertainties.
result The proposed method improves performance on data sets with input uncertainties.
In this short note, we study the injectivity radius bound for three dimensional complete and non-compact Riemannian manifold with good leaf foliations and with bounded curvature up to first order. We obtain the injectivity bound by using the minimal surface theory and the Gauss-Bonnet theorem.
Study lenient regret and good-action identification in Gaussian process bandits.
problem Optimizing function values above a certain threshold in Gaussian process bandits.
method Study lenient regret notions and introduce algorithms for finding good actions.
result Upper and lower bounds on lenient regret for GP-UCB and elimination algorithms.
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coh…
Survey on algebraic minimal cones and nonassociative algebras.
problem Exploring algebraic minimal cones and nonassociative algebras.
method Recollections and recent developments in the field.
result Dedication to Vladimir Miklyukov's memory.
APGAI identifies good arms anytime with fixed budget.
problem Identifying a good arm with a fixed sampling budget.
method An anytime algorithm for good arm identification in stochastic bandits.
result APGAI achieves efficient detection of good arms with upper bounds on probability of error and sampling complexity.
We develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of…
Explains what hierarchically hyperbolic spaces are.
problem None explicitly stated; focuses on definition and understanding.
method Heuristic discussion and detailed technical discussion.
result Provides a mental picture and technical definition of HHSs.
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price opt…
Study on covering probability of random balls in bounded open sets.
problem Probability of covering a bounded open set E with random balls of radius δ. method Geometric conditions and partition of E; lower bounds using good partitions. result Lower bounds to the probability of covering E with balls tend to 1 as Nexp(−δn). Generative models improve commodity hedging using deep learning.
problem Improving risk management in commodity markets.
method Four state-of-the-art generative models adapted for commodity time series.
result Deep hedging of commodity options trained on generated time series shows promising results.
Novel proof technique for Gelfand-Fuks cohomology.
problem Comparing sheaf-like data over manifold Cartesian powers.
method Local-to-global analysis through generalized good covers and factorization algebras.
result Unified approach to Gelfand-Fuks cohomology.
A new bandit problem identifies good arms with minimal samples.
problem Identifying good arms with expected reward above a threshold.
method Stochastic multi-armed bandit problem with exploration-exploitation dilemma.
result Lower bound on sample complexity and efficient algorithm development.
Study tackles online auctions with unknown values, achieving optimal regret bounds.
problem Online auctions with unknown good values and bandit feedback.
method Online learning approach with bandit feedback, stochastic and adversarial models.
result Achieves logarithmic and sublinear regret bounds in both models.
Proposes a method to estimate causal effects over a range of DAGs, addressing uncertainty in prior knowledge.
problem Uncertainty in prior knowledge of causal relationships between variables.
method Gradient-based optimization method providing bounds for causal queries over a collection of causal graphs.
result Bounds achieve good coverage and sharpness for causal queries in various settings.
New model uses heteroscedastic Gaussian process for alkenone SST proxy.
problem Restoring historical sea surface temperatures using proxies.
method Heteroscedastic Gaussian process regression method.
result Nonparametric approach handles variable noise patterns and outliers.
New algorithms handle unpredictable actions in sequential learning.
problem Learning with unreliable composite actions in online optimization.
method Follow-The-Perturbed-Leader method with Counting Asleep Times loss estimation.
result Significant improvement in performance guarantees for sleeping bandit problem.
This paper explores good practices for AI explainability in finance.
problem Complex financial models lack transparency and interpretability.
method Exploring good practices for deploying explainability in AI-based financial systems.
result Developing effective XAI tools for the financial industry.
Framework discovers patient subgroups for better multi-task ICU mortality prediction.
problem Predicting adverse outcomes in heterogeneous ICU patient populations.
method Two-step framework: 1) Unsupervised autoencoder for subgroup discovery, 2) Multi-task learning for separate patient populations.
result Better predictive performance of in-hospital mortality across and within patient groups.
New gossip algorithms estimate U-statistics in networks efficiently.
problem Efficient decentralized estimation of U-statistics in networks.
method Synchronous and asynchronous randomized gossip algorithms.
result Convergence rates of O(1/t) and O(log t / t) for synchronous and asynchronous cases.
Gradient descent achieves good generalization for over-parameterized deep ReLU networks.
problem Understanding good generalization in over-parameterized deep neural networks.
method Algorithm-dependent generalization error bound for deep ReLU networks using gradient descent.
result Gradient descent with proper initialization can achieve arbitrarily small generalization error for over-parameterized DNNs.
The paper tackles robust policy learning in multitask contextual bandits with adversarial users.
problem Learning optimal policies in multitask contextual bandits with a small fraction of adversarial users.
method Developed efficient robust mean estimators for both uni-variate and high-dimensional random variables.
result Lower bound of ildeΩ(min(S,A)⋅α2/ε2) per-user interactions to learn an ε-optimal policy for good users. We discuss construction of coverings of the unit ball of a finite dimensional Banach space. The well known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of good coverings. Here we apply incoherent dictionaries for construction of good cov…
New findings show good representations alone are insufficient for efficient reinforcement learning.
problem Understanding when good representations are enough for efficient reinforcement learning.
method Statistical analysis of reinforcement learning methods, focusing on value-based, model-based, and policy-based learning.
result Hard thresholds for reinforcement learning methods show good representations alone are insufficient, unless they meet certain quality criteria.
Framework learns multiple tasks by sharing features across domains.
problem Learning from small noisy samples and incorporating prior knowledge.
method Modular deep feedforward neural network with shared and private branches.
result Effective domain adaptation and transfer learning demonstrated.
This paper shows how to solve complex reinforcement learning problems with zero duality gap.
problem Complex reinforcement learning problems with conflicting objectives.
method Formulate as a constrained RL problem and solve using Primal-Dual methods.
result The problem has zero duality gap, making it convex and solvable exactly in the dual domain.
This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Using a multivariate normal Copula function for the joint default probabilities we show that retaining the first few moments of the portfolio default l…
Fairly allocate items with noisy queries, reducing envy.
problem Fairly allocate indivisible goods with unknown valuations.
method Use Gaussian noisy queries to find an envy-free allocation.
result The optimal number of queries scales as \( \frac{m^{2.5}}{Δ^2} \) for large negative-envy.
Paper improves EEG signal reconstruction efficiency and accuracy.
problem No good sparse representation and high computational cost in multi-channel EEG signals.
method Proposes an optimization model with L0 norm and Schatten-0 norm for cosparsity and low rank structures, using convex relaxation and alternating direction method of multipliers.
result Improves multi-channel EEG signal reconstruction in terms of accuracy and computational complexity.
Proposes a method for explaining ranking decisions in learning systems.
problem Limited work on interpreting ranking decisions from learning systems.
method Model agnostic local explanation method using optimization to maximize validity.
result Approach outperforms other methods in validity across different LTR models.
Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
Paper proposes a method to aggregate Bayesian networks from multiple datasets.
problem Aggregating Bayesian networks from separate data sets.
method Gaussian Bayesian network fusion method.
result Method obtains good results and surpasses individual learning.