Study of participating policies with guaranteed minimum interest rate and surrender option.
problem Analyzing the value and optimal surrender strategy of participating policies with minimum interest rate guarantee and surrender option.
method Probabilistic analysis using optimal stopping and free boundary theory.
result Identification of an optimal surrender strategy involving stop-loss and too-good-to-persist boundaries.
A variable annuity is an equity-linked financial product typically offered by insurance companies. The policyholder makes an upfront payment to the insurance company and, in return, the insurer is required to make a series of payments starting at an agreed upon date. For a higher premium, many insurance companies offer…
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the contract plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal(dynamic) withdrawal strategy of a policyh…
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…
Enhances valuation of variable annuities with stochastic interest rate models.
problem Valuation and optimal surrender strategies for variable annuities in Lévy models.
method Hybrid numerical method combining tree methods for interest rate modeling and finite difference techniques for asset price.
result Influence of stochastic interest rates on surrender decisions and contract design.
The paper analyzes GMWB annuities in low interest rate environments.
problem Valuation of GMWB annuities in low interest rate conditions.
method Dynamic programming and Hull-White interest rate model.
result Low interest rates increase the fair value of GMWB annuities.
Develops a new method for pricing GMWBs with jumps and stochastic interest rates.
problem Pricing guaranteed minimum withdrawal benefits (GMWBs) with jumps and stochastic interest rates.
method Combines semi-Lagrangian method with Fourier pricing and Green's function.
result Mathematically demonstrates convergence to the viscosity solution of the HJB-QVI.
Valuing Guaranteed Minimum Withdrawal Benefit (GMWB) has attracted significant attention from both the academic field and real world financial markets. As remarked by Yang and Dai, the Black and Scholes framework seems to be inappropriate for such a long maturity products. Also Chen Vetzal and Forsyth in showed that th…
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 presents deep LSMC method for efficient variable annuity pricing.
problem Efficiently pricing variable annuities with guarantees using simulation methods.
method Modifies least-squares Monte Carlo (LSMC) algorithm for optimal stochastic control problems.
result Deep LSMC provides more stable and robust pricing performance for higher-dimensional problems.
Optimal student loan repayment strategies vary based on loan size.
problem Finding the most cost-effective repayment strategy for federal student loans.
method Analyzing the impact of different repayment strategies on total cost for varying loan sizes.
result Optimal repayment strategies depend on the loan balance, with different approaches for small, large, and intermediate balances.
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.
Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest rates between maturities in the discrete tenor structure is equivalent to ext…
The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by no…
Minimum Description Length prevents overfitting in noisy data.
problem Learning from noisy data with overfitting risk.
method Minimum Description Length learning rule with tempered guarantees.
result Tempered agnostic finite sample learning guarantees and asymptotic behavior characterization.
AdaLoss optimizes adaptive learning rates for efficient convergence in various models.
problem Efficiently optimizing adaptive learning rates for gradient descent methods.
method AdaLoss uses loss function information to dynamically adjust step sizes.
result AdaLoss achieves linear convergence in linear regression and robust global convergence in neural networks.
Paper relaxes factor analysis for noisy data, improving robustness.
problem Challenges in finding robust low dimensional approximations for data with heteroskedastic noise.
method Introduces a relaxed version of Minimum Trace Factor Analysis (MTFA) as a convex optimization method.
result Effective at not overfitting to heteroskedastic perturbations and addressing common issues in factor analysis.
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of d=nα, α∈(0,1), for the input dimension d and sample size n. Empirical evidence supports our finding that minimum-norm interpo…
In this paper we investigate price and Greeks computation of a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochastic interest rate are considered together in the Heston Hull-White model. We consider a numerical method the solves the dynamic control problem due…
The study identifies features making cross-impact relevant in explaining price variance of US assets.
problem Understanding the relevance of cross-impact in explaining price variance of US assets.
method Using tick-by-tick data spanning 5 years for 500 US assets, the study investigates the features making cross-impact relevant.
result Price formation is endogenous within highly liquid assets, influencing less liquid correlated products with a constrained impact velocity.
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the …
Insurance companies often include very long-term guarantees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (G.A.O), the insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rated when the policy matures. Both …
Paper provides a performance guarantee for spectral clustering.
problem Finding the global solution to the minimum ratio cut problem.
method Two-step spectral clustering method with a rounding step, analyzed using two-to-infinity norm perturbation bounds.
result Spectral clustering is guaranteed to output the global solution under certain conditions.
We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover, to have a minimum guarantee for the final annuity, a safety level for the wealt…
Adaptive learning rates improve FTPL's BOBW guarantees in bandit problems.
problem Improving Follow-the-Perturbed-Leader's BOBW guarantees in bandit problems.
method Introducing surrogate probability functions to compute adaptive learning rates without exact probabilities.
result BOBW guarantees for FTPL with Pareto perturbations for any α>1. The paper analyzes convergence in SGD with momentum and proposes a diagnostic test.
problem Detecting convergence in stochastic gradient descent with momentum.
method Analyzes the transient and stationary phases of SGD with momentum, constructs a statistical diagnostic test.
result The proposed diagnostic test effectively detects convergence in the stationary phase of SGD with momentum.
A scenario in which regulators take the drastic step of requiring coverage of all venture bank investment loans using interbank borrowed funds is considered. In this scenario, a minimal amount of default insurance is used, such that Tier 1 and 2 capital requirements are still met. To do this, the default insurance perc…
Paper establishes generalization bounds for representation learning using Minimum Description Length.
problem Designing efficient statistical supervised learning algorithms that generalize well to unseen data.
method Developed a compressibility framework using Minimum Description Length (MDL) to derive upper bounds on generalization error.
result Established the first theoretical generalization bounds for Information Bottleneck type encoders and representation learning.
We consider the problem of downlink power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To mitigate the interference among concurrent transmissions, we leverage the network topology to create a graph neural network arc…
In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification error of the majority-vote classifier with the average individual …
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…
New insights into learning for blind inverse problems with theoretical guarantees.
problem Learning in blind inverse problems where both signal and operator are unknown.
method Data-driven approaches using Linear Minimum Mean Square Estimators (LMMSEs) with theoretical analysis.
result Established equivalences with Tikhonov-regularized formulations and derived finite-sample error bounds.
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to…
TD(0) with Polyak-Ruppert averaging achieves robust and fast convergence rates
problem TD(0) learning under Markovian sampling
method Polyak-Ruppert averaging with a single stepsize
result Simultaneous high-probability convergence guarantees for TD(0) iterates and PR average
Theoretical study shows AI models can recover from contaminated training data.
problem Data contamination in AI training can degrade model performance.
method Theoretical analysis and experiments on various data types.
result Models converge to true distribution under mild conditions, with rate dependent on real data fraction.
In the present paper we provide a two-step principal protection strategy obtained by combining a modification of the Constant Proportion Portfolio Insurance (CPPI) algorithm and a classical Option Based Portfolio Insurance (OBPI) mechanism. Such a novel approach consists in assuming that the percentage of wealth invest…
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tra…
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in the correlated environment is a challenging task and no closed form solution exis…
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.
The success of deep learning in numerous application domains created the de- sire to run and train them on mobile devices. This however, conflicts with their computationally, memory and energy intense nature, leading to a growing interest in compression. Recent work by Han et al. (2015a) propose a pipeline that involve…
Proposes a new feature selection method integrating feature relationships.
problem Feature selection in machine learning models.
method Integrates feature-feature and feature-target relationships via penalized mRMR.
result Correctly identifies inactive features, reducing false discoveries.
This paper improves indoor positioning accuracy by deploying reference nodes to ensure Line-of-Sight.
problem Systematic bias errors in indoor positioning due to non-LoS propagation.
method Model indoor service area as a graph, partition into cliques for reference nodes, set minimum distance and angle parameters.
result Guaranteed LoS to reference nodes improves indoor positioning accuracy and precision.
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
New framework for DNN training guarantees convergence to global minimum.
problem Training deep neural networks to converge to global minimum.
method Reformulated minimization problem with recursive algorithmic framework, using bounded style assumptions.
result Convergence to an ε-(global) minimum with O(1/ε^3) gradient computations.
FedAvg converges linearly to global minimum in federated learning with partial participation.
problem Challenges in federated learning with partial client participation.
method Federated averaging (FedAvg) method for over-parameterized neural networks.
result FedAvg converges to global minimum at a linear rate after t iterations.
Study introduces AMVP and AMRR for dynamic portfolio optimization in volatile markets.
problem Optimizing portfolios in volatile and nonstationary financial markets.
method Adaptive Minimum-Variance Portfolio (AMVP) framework with ARFIMA-FIGARCH processes and non-Gaussian innovations.
result Demonstrated superior performance in risk reduction and portfolio stability during market breaks.
We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …
New convergence rates found for PnP methods using MMSE denoisers.
problem Asymptotic convergence of PnP methods with MMSE denoisers.
method Explicitly represented MMSE denoiser as an upper Moreau envelope, derived sublinear convergence rates.
result First sublinear convergence guarantee for PnP proximal gradient descent with MMSE denoiser.