The paper studies variable annuity benefits using exponential functionals of Levy processes.
problem Modeling equity returns with a Levy process to better fit market features.
method Uses exponential functionals of a Levy process to compute the distribution of variable annuity guaranteed benefits.
result Explicitly computes the distribution of certain exponential functionals.
Paper explores how to design federated learning protocols that benefit all participants while maintaining privacy.
problem Privacy concerns undermine the accuracy benefits of federated learning in privacy-sensitive domains.
method The paper provides conditions for mutually beneficial federated learning protocols and designs protocols that maximize total utility and accuracy.
result The paper demonstrates that federated learning can be designed to be mutually beneficial, striking a balance between privacy and model accuracy.
In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behaviour solved as an optimal stochastic control problem. This product simultaneously deals with financial risk, mortali…
Study validates Libor model for insurance benefits calculation.
problem Valuation of long-term insurance guarantees.
method Mean-field Libor market model, numerical ALM, aggregated life insurance data.
result Derives estimators for future discretionary benefits.
Research examines GMIB and reset options in variable annuities.
problem Understanding the value and rationality of GMIB and reset options.
method Exploration of various parameters affecting GMIB value and calculation of critical future interest rates for reset option rationality.
result Insight into how future market performance and interest rates influence policyholder and insurer actions.
New DP algorithms with margin guarantees for various hypothesis sets.
problem Differential privacy in machine learning with margin guarantees.
method Developed pure and efficient DP learning algorithms for linear, kernel-based, and neural network hypotheses.
result Margin guarantees are independent of input dimension and hypothesis type.
Investigates optimal withdrawal strategies in VA contracts with tax and ratchet mechanisms.
problem Optimizing withdrawal strategies and behavior of policyholders in VA contracts with tax and ratchet mechanisms.
method Solving a backward dynamic programming problem to optimize cash flows from VA contracts, considering hybrid products and taxation effects.
result Tax-shielding effect of the cash fund enhances contract attractiveness, ratchet mechanism discourages early surrender, and cash fund discourages active withdrawals.
Unified pricing method for variable annuity guarantees using stochastic control.
problem Pricing variable annuity guarantees for retail investors.
method Optimal stochastic control framework, direct integration method with spline interpolation.
result Efficient numerical method for pricing variable annuity guarantees.
We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore,…
Unified surrogate loss framework for multi-label learning with strong consistency guarantees.
problem Improving consistency and accounting for label correlations in multi-label learning.
method Introducing multi-label logistic loss and extending it to comprehensive multi-label comp-sum losses, proving strong consistency guarantees for any multi-label loss.
result Unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss.
Researchers develop CG for deep learning constraints, improving model efficiency and accuracy.
problem Training deep neural networks with global constraints.
method Revisit Conditional Gradients (CG) for handling deep learning constraints.
result Convergence guarantees and immediate benefits in training ResNets and GANs.
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
Paper proves IRLS converges to subspace from any start, with practical benefits.
problem Robust subspace estimation in machine learning.
method Iteratively Reweighted Least Squares (IRLS) with dynamic smoothing regularization.
result IRLS converges linearly to the underlying subspace from any initialization under deterministic conditions.
In this paper we explore an identity in distribution of hitting times of a finite variation process (Yor's process) and a diffusion process (geometric Brownian motion with affine drift), which arise from various applications in financial mathematics. As a result, we provide analytical solutions to the fair charge of va…
Investigates the benefits of multi-head attention in Transformers, deriving convergence and generalization guarantees.
problem Underexplored dynamics of multi-head attention in Transformer training and generalization.
method Derives convergence and generalization guarantees for gradient-descent training of a multi-head self-attention model.
result Establishes conditions for initialization that ensure multi-head attention's realizability.
Paper presents online learning for statistical arbitrage without stationarity assumptions.
problem Statistical arbitrage strategies often rely on assumptions that may not hold for non-stationary processes.
method Online learning algorithms for mean reversion models without stationarity assumptions.
result Strong learning guarantees for online learning in non-stationary processes.
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the admissible set. Often, such contracts specify that the holder exert control at a…
PAC-Wrap provides provable guarantees for semi-supervised anomaly detection.
problem Ensuring reliable anomaly detection in safety-critical applications.
method PAC-Wrap wraps around existing anomaly detection methods to provide PAC guarantees.
result PAC-Wrap effectively provides rigorous guarantees for various anomaly detectors.
The paper studies the benefits of curriculum learning in linear regression tasks.
problem Theoretical understanding of curriculum learning's benefits in machine learning.
method Theoretical analysis of curriculum learning in structured and unstructured multitask linear regression problems.
result Adaptive learning in the unstructured setting is fundamentally harder than oracle learning, but not in the structured setting.
Reinsurance can help life insurers maintain higher capital guarantees without losing utility.
problem Decreasing capital guarantees in life insurance products.
method Dynamic investment-reinsurance optimization problem with simultaneous Value-at-Risk and no-short-selling constraints. Introduced guarantee-equivalent utility gain for comparison.
result Optimally managed reinsurance allows insurers to offer higher capital guarantees without reducing expected utility.
The paper provides theoretical guarantees for optimized sampling in compressed sensing, showing error vanishes with more measurements.
problem Theoretical and practical improvements in compressed sensing with optimized sampling schemes.
method Theoretical analysis and empirical experiments with optimized sampling schemes for subsampled unitary matrices.
result The error caused by measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming Gaussian noise.
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We first present a series of new regret guarantees that hold at any time and under …
The paper offers a new model for variable annuities with surrender risk.
problem Modeling variable annuities with surrender risk and market consistency.
method Hybrid model with Lévy processes, time-inhomogeneous, and dependence between financial and surrender risks.
result Explicit analytical formulas and practical numerical procedures for variable annuity valuation.
Privacy-preserving SGD with heavy-tailed noise achieves differential privacy guarantees.
problem Privacy preservation in noisy SGD with heavy-tailed noise.
method Differential privacy guarantees for SGD with heavy-tailed noise.
result SGD with heavy-tailed perturbations achieves (0,O(1/n))-DP. Binary funding impacts simplify derivative pricing models.
problem Complexity in derivative pricing due to varying lending/borrowing rates.
method Analyzes the binary nature of funding impacts leading to linear or semi-linear equations.
result Derivatives pricing simplifies when only one rate affects the payoff function.
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum likelihood estimates from corrupted or incomplete data. The convergence speed-up is an e…
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insur…
Pension benefits valuation with Florida second election and DB Underpin options.
problem Valuation of hybrid pension benefits with embedded options.
method Arbitrage-free pricing methodology to value Bermudan options.
result Illustrates the difference between FSE, DB Underpin, and Bermudan DB Underpin options.
Paper proves minibatch SGD for GP inference converges and improves generalization.
problem Theoretical understanding and practical use of SGD for correlated samples in Gaussian process inference.
method Proves minibatch SGD converges to a critical point with rate O(1/K) for K iterations, under certain kernel conditions.
result Minibatch SGD for GP inference improves generalization and reduces computational burden.
New algorithms and guarantees for multiple-source adaptation.
problem Improving model performance on target mixtures from multiple sources.
method Normalized solutions with theoretical guarantees, algorithms for distribution-weighted combination.
result Our algorithm outperforms competing approaches by producing a robust model.
New RL algorithms improve control tasks with data reuse.
problem Real-world control requires performance guarantees and data efficiency.
method Generalized Policy Improvement combining on-policy guarantees and sample reuse.
result Extensive experimental analysis shows benefits of new algorithms.
Study shows algorithms benefit from limited target data with many source domains.
problem Adapting to new domains with scarce labeled target data.
method New family of model selection algorithms.
result Beneficial guarantees in scenarios with limited target data.
Paper provides first theoretical guarantees for hyperbolic space learning.
problem Learning a classifier in hyperbolic space for hierarchical data.
method Efficient algorithm for large-margin hyperplane learning in hyperbolic space.
result The low embedding dimension in hyperbolic space leads to superior classifier learning guarantees.
Paper assesses GMMB in VAs using FST for accurate net liability calculations.
problem Risk management of GMMB under stochastic mortality and regime-switching.
method Net liability model with FST algorithm for accurate numeric solutions.
result FST algorithm provides reliable results for net liability of GMMB.
New pension design reduces volatility without guarantees.
problem Pension volatility and guarantees issues.
method Split premium, invest in funds, redistribute to smooth volatility.
result Maximizes total accumulated capital at retirement.
Monotonicity helps in safely optimizing unknown functions.
problem Sequentially maximizing an unknown function with safety constraints.
method Gaussian process with monotonicity assumption, inspired by GP-UCB and SafeOpt.
result The proposed M-SafeUCB algorithm achieves theoretical guarantees and safety.
New algorithm tackles online optimization with non-additive constraints, achieving dynamic regret guarantees.
problem Online optimization with non-stationary and long-term constraints in display advertising.
method Online primal-dual algorithm with dynamic cumulative regret guarantees.
result Dynamic cumulative regret guarantees depend on penalty convexity, smoothness, and residual smoothness.
Paper develops an efficient algorithm for pricing GMWB contracts under stochastic interest rates.
problem Valuation of Variable Annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rates.
method Developed an efficient new algorithm for pricing GMWB contracts using backward recursion and high-order Gauss-Hermite quadrature.
result The new algorithm is significantly faster than finite difference or Monte Carlo methods for pricing GMWB contracts.
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…
Constructs tail-specific prediction intervals for financial applications
problem Financial applications require strict control on the left tail
method Extends classical conformal frameworks to provide explicit tail-specific guarantees
result Improved directional calibration in skewed data
Variable annuities (VA) are popular insurance products. VAs provides the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if returns of underlying funds are high enough. Here we consider a special case of VA with high-water mark feature and Gua…
Theoretical guarantees for neural estimators in parametric statistics are derived.
problem Lack of theoretical guarantees for neural estimators in parametric statistics.
method Decompose risk into terms and verify assumptions for convergence.
result Derive theoretical guarantees for neural estimators.
We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the final excess risk will compare favorably with utilizing the entire original dat…
AUASE embeds dynamic networks with stability guarantees for node comparison.
problem Stability in dynamic network embeddings for comparing nodes across time.
method Attributed unfolded adjacency spectral embedding (AUASE) for stable unsupervised learning.
result AUASE provides significant improvements in link prediction and node classification.
Random classifier ensembles improve fairness and diversity in decision making.
problem Loss of diversity and fairness in single machine learning classifiers.
method Study of random classifier ensembles for fairness-aware learning.
result Ensemble of classifiers can achieve better fairness and accuracy trade-offs.
New framework quantifies learning guarantees for inconsistent convex surrogates.
problem Analyzing consistency properties of machine learning methods with inconsistent convex surrogates.
method Extending the framework of Osokin et al. (2017) to inconsistent surrogates, introducing a new lower bound on the calibration function.
result Shows how learning with inconsistent surrogates can have guarantees on sample complexity and optimization difficulty.
Improves continual learning with theoretical guarantees and a new algorithm.
problem Learning incremental tasks with dynamic data distributions.
method Contrastive and distillation losses with theoretical performance guarantees.
result Theoretical performance bounds and improved continual learning performance.
This work improves robustness guarantees for neural networks using low rank representations.
problem Certified robustness to adversarial perturbations in neural networks.
method Low rank representations to provide improved robustness guarantees.
result Improved robustness guarantees for ℓ∞ perturbations using natural low rank representations.