Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
Enhances financial risk quantification in classical models.
problem Risk quantification in classical finance models.
method Nested risk measures, limiting behavior analysis.
result Uniqueness of risk-averse limit in classical models.
New method reduces CVA-VaR computation complexity.
problem Efficiently estimating CVA-VaR for financial risk management.
method Multilevel nested simulation for probabilities.
result 3 orders of magnitude reduction in computational complexity.
Improved MLMC method boosts risk estimation efficiency.
problem Estimating risk measures like Value-at-Risk in financial risk management.
method Novel MLMC parametrization and antithetic sampling.
result Significantly improved performance in practical settings.
Proposes a new framework for risk-sensitive RL using deep nets.
problem Risk-sensitive reinforcement learning problems.
method Conditional elicitability, scoring functions, deep neural networks.
result Dynamic spectral risk measures can be approximated by deep nets.
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
We investigate the problem of computing a nested expectation of the form P[E[X∣Y]≥0]=E[H(E[X∣Y])] where H is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfo…
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the impact of input uncertainty on output response has been extensively studied. Most…
Paper establishes identifiability and elicitability of tail risk measures.
problem Identifying and measuring tail risk measures accurately.
method Establishes identifiability and elicitability of tail risk measures using generators and quantiles.
result Joint identifiability and elicitability of tail risk measures and quantiles.
A new method sorts models to find the best one with minimal risk.
problem Finding the best model with minimal risk among nested models.
method Nested Empirical Risk (NER) and Sorted NER (S-NER) methods.
result The S-NER method selects the true model order and the most parsimonious model.
A new method for efficient nested Monte Carlo simulations in financial modeling.
problem Computational challenges in nested stochastic modeling for financial risk assessment.
method Sample recycling approach to speed up inner loop estimations.
result Significantly more efficient than traditional techniques.
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we s…
Study quantifies information borrowing in hierarchical Bayesian models.
problem Impact of shared hyperparameters on posterior inference.
method Non-asymptotic framework, nested hierarchical prior distribution, integrated risk measure.
result Deeper hierarchical models outperform nested ones under certain conditions.
A new algorithm estimates VaR and ES for financial risks.
problem Estimating Value-at-Risk and Expected Shortfall for financial losses.
method Multilevel Stochastic Approximation (MLSA) scheme for nested stochastic approximation problems.
result Optimal complexities for VaR and ES estimation are derived.
Proposes methods for online conformal prediction with nested prediction sets across multiple confidence levels.
problem Need for uncertainty quantification with multiple confidence levels in diverse applications.
method Online optimization perspective to enforce nestedness of prediction sets while controlling quantile estimation error.
result Achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency.
The paper proposes a decoupled approach to efficiently estimate CoVaR, a measure of systemic financial risk.
problem Estimating CoVaR, a measure of systemic financial risk, is challenging due to zero-probability events and portfolio repricing.
method The paper introduces a decoupled approach using smoothing techniques and a functional perspective to model CoVaR.
result The decoupled estimator achieves a rate of convergence of approximately OmP(Γ−1/2). Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and (b) evaluating the loss of the portfolio is expensive and the …
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variabl…
Paper tackles robust optimization under uncertainty using nested distance.
problem Optimizing under distributionally robust uncertainty with nested distance.
method Equivalent recursive and dynamic programming reformulations for tractable optimization.
result Optimal robust policies can be found efficiently using convex optimization.
By specifying model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and tempera…
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distrib…
BAxUS optimizes high-dimensional functions adaptively, avoiding performance degradation and failure.
problem State-of-the-art HDBO methods degrade or fail with increasing dimensions.
method BAxUS uses nested random subspaces to adaptively optimize high-dimensional functions.
result BAxUS outperforms state-of-the-art methods across various applications.
The paper uses LSM to solve complex monetary utility functions.
problem Computing dynamic monetary utility functions with high dimensions.
method Least Squares Monte Carlo (LSM) algorithm.
result LSM algorithm successfully applied to recursive Cost-of-Capital valuation.
Improves test set performance and reduces out-of-sample disappointment for unstable models.
problem Ensuring strong test set performance via cross-validation for unstable models.
method Nested k-fold cross-validation with hyperparameter selection based on a weighted sum of cross-validation metric and model stability measure.
result Improves out-of-sample MSE for sparse ridge regression and CART by 4% and 2% respectively, compared to k-fold cross-validation.
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.
Review of MLMC in financial engineering, focusing on option pricing and risk management.
problem Efficient estimation of financial risks and option prices using Monte Carlo methods.
method Incorporation of importance sampling and adaptive sampling algorithms in MLMC framework.
result Hybrid algorithms reduce overall variance in estimating financial risks and option prices.
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of multi-dimensional stochastic processes. Except in the simplest cases, no closed-form expressi…
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
Study improves predictive performance testing for high-dimensional data using exhaustive nested cross-validation.
problem Reproducibility issues in K-fold cross-validation for high-dimensional data. method Proposes a novel predictive performance test based on exhaustive nested cross-validation, addressing computational complexity with a closed-form expression.
result Demonstrates the effectiveness of Ridge-based methods in high-dimensional predictive performance testing.
New method estimates nested expectations with biased and antithetic sampling.
problem Estimating nested expectations with biased and antithetic sampling.
method Nested multilevel Monte Carlo with biased and antithetic sampling.
result Estimator achieves order ε^(-2) asymptotic cost.
This paper uses Nested Sampling to improve Gaussian Process uncertainty quantification.
problem Underestimating predictive uncertainty and overfitting in Gaussian Process models.
method Marginalises hyperparameters using Nested Sampling for spectral mixture kernels.
result Improves predictive performance and uncertainty quantification across various data sets.
We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via VaR or TVaR of a given collection of future economic scenarios representing factor…
The paper proposes an efficient nested simulation design using likelihood ratio method.
problem Designing nested simulations with fixed outer scenarios and minimizing simulation effort.
method Proposes a bi-level optimization problem to decide inner replications and pooling strategies.
result Optimized design achieves $\cO(Γ^{-1})$ mean squared error of estimators.
The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force "Monte-Carlo of Monte-Carlo" method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm le…
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…
The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with variable errors, and deriving parameter uncertainties is often an after-th…
A deep BSDE approach tackles multi-layered xVA calculations for portfolio valuation.
problem Computational intractability in nested simulations for multi-layered xVA calculations.
method Iterative deep BSDE approach, change-of-measure method, quantile regression for margin computation.
result Reduces computational demands and successfully scales to high-dimensional portfolios.
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Mon…
Study develops efficient nested deep hedging method for derivatives pricing.
problem Hedging derivatives in market frictions using multiple options.
method Nested deep hedging approach with efficient learning techniques.
result Reduces arbitrage opportunities and improves hedging risks.
Novel AMM model for pegged cryptoassets using nested OU processes.
problem Liquidity and risk management in markets for pegged cryptoassets.
method Multi-level nested Ornstein-Uhlenbeck (OU) processes for exchange rate dynamics, calibrated and filtered AMM model.
result Consistent efficient quotes and improved liquidity provision for pegged cryptoassets.
Study cobordisms of nested manifolds and their invariants.
problem Understanding cobordisms of nested manifolds and their invariants.
method Identify a nested analog of the Pontryagin-Thom construction and find spaces homotopy equivalent to nested Pontryagin-Thom spaces.
result Discover nested cobordism invariants and provide an alternative proof of Wall's splitting result.
Novel approach to Bayesian experimental design for non-exchangeable data.
problem Optimal experimental design for non-exchangeable data.
method Inside-Out SMC2 algorithm embedded in particle Markov chain Monte Carlo framework. result Efficacy demonstrated on a set of dynamical systems.
Study tests how U.S. equity prices align with global asset frequencies using financial variables.
problem Testing whether U.S. equity prices align with global asset frequencies using financial variables.
method Examines SPX and RUT gaps, uses OIS-based funding, volatility, trading-friction, financial-condition variables, and residual information.
result Gains in fit survive broad-dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection, supporting reduced-form P-Q alignment.
We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is possible and we give an efficient sampling algorithm. The combination of these two pr…
We give a simple explicit algorithm for building multi-factor risk models. It dramatically reduces the number of or altogether eliminates the risk factors for which the factor covariance matrix needs to be computed. This is achieved via a nested "Russian-doll" embedding: the factor covariance matrix itself is modeled v…
We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form formulation admits an analytical solution, to the optimal leverage…
We introduce a multi-factor stochastic volatility model for commodities that incorporates seasonality and the Samuelson effect. Conditions on the seasonal term under which the corresponding volatility factor is well-defined are given, and five different specifications of the seasonality pattern are proposed. We calcula…