A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “Conditional Expectation”
Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
Automatic Backward Differentiation for American Monte-Carlo Algorithms (Conditional Expectation)q-fin.CP
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan product valuation, but the method is applicable in full generality. The method …
New unbiased gradient estimators for complex optimization problems.
problem Unbiased and variance-limited gradient estimation for conditional stochastic optimization.
method Developed multilevel Monte Carlo gradient estimators for conditional stochastic optimization problems.
result Unbiased and finite variance gradient estimators for conditional stochastic optimization problems.
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random variables in the combination. It turns out that under suitable conditions on the join…
Paper tackles conditional expectation estimation using compactification operators.
problem Estimating conditional expectations from product of two random variables.
method Operator theoretic approach using kernel integral operators in reproducing kernel Hilbert space.
result Solutions allow numerical approximation and convergence of data-driven implementations.
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
Novel approach for estimating conditional expectations using Bayesian quadrature.
problem Estimating conditional expectations with costly evaluations.
method Probabilistic numerical methods incorporating prior smoothness knowledge.
result Fast convergence rate and uncertainty quantification.
Scalable method for Bayesian experimental design without integrating over posterior distributionmath.NA
Efficiently designs experiments without integrating posterior distributions.
problem Computational inefficiency in Bayesian experimental design for PDE-based models.
method Likelihood-free approach using ANN to approximate conditional expectation.
result Significant reduction in observation model evaluations.
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques o…
The article analyzes LCE in Hilbert space, deriving new formulas and regularisation methods.
problem Analyzing conditional expectation in infinite-dimensional Hilbert space.
method Establishing analytical properties and regularisation for LCE in Hilbert space, deriving new formulas.
result Simple derivation and intuitive justification of conditional mean embedding formula.
A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.
problem Calculating cross valuation adjustments (XVA) in realistic financial scenarios.
method Simulation/regression scheme for BSDEs, using neural networks and quantile regressions.
result The scheme outperforms Picard iterations in high-dimensional and hybrid market risks.
This paper discusses an alternative explanation for the empirical findings contradicting the positive relationship between risk (variance) and reward (expected return). We show that these contradicting results might be due to the false definition of risk-perception, which we correct by introducing Expected Downside Ris…
Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propag…
This paper rethinks confidence calibration under covariate shifts.
problem Calibration methods struggle with covariate shifts and unstable importance weighting.
method Derives Expectation consistency condition and proposes Expectation consistency loss (ECL).
result ECL loss is compatible with various types of calibration and has the same sample complexity as ECE.
A neural network approach for efficient conditional SHAP calculations.
problem Efficiently calculating conditional SHAP values for various models.
method Surrogate neural network approach for conditional SHAP.
result Efficiently calculates conditional SHAP values for neural networks and other regression models.
Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensionsstat.ME
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
This paper deals with multidimensional dynamic risk measures induced by conditional -expectations. A notion of multidimensional -expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
Defines -expectation of distributions and its applications.
problem Defining -expectation of distributions.
method Two special cases of nonlinear and law-invariant -expectation.
result Explicit derivation of -expectation of distributions.
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail Expectation describes the expected amount of risk that can be experienced given …
On the coherence of Expected Shortfallcond-mat.stat-mech
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
Paper proposes using tree-based surrogate models for efficient Shapley computation.
problem Efficient computation of Shapley values using conditional expectations.
method Surrogate model-based tree for approximating Shapley and SHAP values.
result The proposed algorithm improves accuracy and unifies global interpretation.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in is defined as the best -estimate, given a -subalgebra and a degree of model uncertainty. When the random vector represents the payoff…
Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we prop…
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
Paper improves VaR risk allocation by avoiding zero probability events.
problem Computing VaR contributions for zero probability events.
method Reformulates Euler contributions to a ratio of conditional expectations with strictly positive probability events.
result Proposed estimator outperforms standard Monte Carlo methods in bias and variance.
We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditi…
The paper defines and characterizes conditional nonlinear expectations.
problem Defining and characterizing conditional nonlinear expectations.
method Embedding in decision theory, using state-dependent preferences, and continuous utility representation.
result Consistent backward conditional projections are characterized by the Sure-Thing Principle.
Stochastic Gradient Descent with Exponential Convergence Rates of Expected Classification Errorsstat.ML
We consider stochastic gradient descent and its averaging variant for binary classification problems in a reproducing kernel Hilbert space. In the traditional analysis using a consistency property of loss functions, it is known that the expected classification error converges more slowly than the expected risk even whe…
Financial Resilience Evaluation: From Conditional Expectations to Dynamic Convex Risk Measuresq-fin.MF
Enhances resilience evaluation by using dynamic convex risk measures.
problem Capturing the full risk profile of financial positions under adverse conditions.
method Introduces a new resilience evaluation method using dynamic convex risk measures.
result Shows that the resilience evaluation can distinguish between positions with the same expected recovery but different conditional risk profiles.
The paper uses regression trees/random forests to price Bermudan options more efficiently.
problem Pricing Bermudan options with conditional expectation estimation.
method Estimates conditional expectations using regression trees or random forests instead of traditional regression methods.
result Regression trees/random forests provide better results in high dimensions.
Noise Contrastive Meta-Learning for Conditional Density Estimation using Kernel Mean Embeddingsstat.ML
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional distributions which cannot be meaningfully summarized using expectation only (due to e…
We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return unde…
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry and academia, mainly due to analytical tractability reasons. We complete the sto…
Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfallq-fin.RM
A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and the latent conditional expectile. Nonlinear threshold specification is further i…
Investigates conditions for risk or utility functionals to be sensitive to large losses.
problem Conditions for risk or utility functionals to be sensitive to large losses.
method Analyzes sensitivity to large losses for various risk and utility functionals.
result Value at Risk and Expected Shortfall generally fail to be sensitive to large losses, but expected utility functionals and certain adjusted versions are sensitive.
Develops methods to estimate ratios of conditional expectation functions.
problem Estimating ratios of conditional expectation functions in causal inference.
method Orthogonal series estimator combined with debiased machine learning techniques.
result Valid pointwise and uniform asymptotic results for estimation and inference on CEFR.
A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Themstat.ML
New methods for estimating conditional Shapley values compared and evaluated.
problem Estimating precise conditional Shapley values for tabular data models.
method Developed new and extended methods using Monte Carlo integration and regression.
result Recommendations for choosing between Monte Carlo and regression methods based on data distribution.
New methods solve SPDEs for financial derivative pricing.
problem Deriving the price of financial derivatives using SPDEs.
method Developed a conditional Feynman-Kac formula to solve SPDEs.
result Established new numerical methods for mixed Monte-Carlo PDEs.
The paper extends asset pricing theory by considering conditional markets.
problem Analyzing financial markets with conditional information.
method Time consistency properties of dynamic nonlinear expectations applied to super- and subhedging prices.
result Derives a conditional version of the second fundamental theorem of asset pricing.
The paper generalizes Feynman-Kac formula for volatility uncertainty.
problem Calculating sublinear expectation under volatility uncertainty.
method Generalization of Feynman-Kac formula under different hypotheses.
result G-conditional expectation is a viscosity solution of a nonlinear PDE.
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.
Calculating Value-at-Risk contributions in CreditRisk+cond-mat.stat-mech
Credit Suisse First Boston (CSFB) launched in 1997 the model CreditRisk+ which aims at calculating the loss distribution of a credit portfolio on the basis of a methodology from actuarial mathematics. Knowing the loss distribution, it is possible to determine quantile-based values-at-risk (VaRs) for the portfolio. An o…