Paper: arXiv 2503.17737

Abstract

Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evaluations of the expensive-to-evaluate objective function. The proposed algorithm’s competitive performance is demonstrated through practical examples.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts including Bayesian Optimization, Gaussian Processes, and risk measures like CVaR, requiring dense derivations and formal theorems. It also includes practical numerical examples and algorithm performance comparisons, indicating strong empirical implementation and data-driven validation.

Research Flowchart

  flowchart TD
  A["Research Goal: Minimize CVaR<br>for portfolio optimization"] --> B["Input: Historical Asset Returns &<br>Minimum Expected Return Constraint"]
  B --> C["Methodology: Bayesian Optimization<br>with new acquisition function"]
  C --> D{"Two-stage evaluation<br>procedure?"}
  D -- Yes --> E["Reduced evaluations of<br>expensive CVaR function"]
  D -- No --> F["Standard CVaR<br>evaluations"]
  E --> G["Key Outcomes: Achieved<br>optimal risk allocation<br>with fewer computations"]
  F --> G
  G --> H["Result: Competitive performance<br>demonstrated in practical examples"]

Cited References (395)

  1. Multi-task bayesian optimization (2013)
  2. Bayesian optimization for policy search via online-offline experimentation (2019)
  3. High-dimensional contextual policy search with unknown context rewards using Bayesian optimization (2020)
  4. Offline contextual bayesian optimization (2019)
  5. Contextual gaussian process bandit optimization (2011)
  6. Maximal subgroups of finite genus (1985)
  7. Bayesian optimization (2018)
  8. Bayesian optimization (2023)
and 387 more
  1. Optimization of a supply portfolio in the context of supply chain risk management: literature review (2018)
  2. A new hybrid risk-averse best-worst method and portfolio optimization to select temporary hospital locations for Covid-19 patients (2023)
  3. Portfolio optimization of energy communities to meet reductions in costs and emissions (2019)
  4. Collected Papers, Volume III (1972)
  5. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking (2002)
  6. A fresh look at multicanonical Monte Carlo from a telecom perspective (2009)
  7. Sequential monte carlo samplers (2006)
  8. A tutorial on particle filtering and smoothing: Fifteen years later (2009)
  9. Monte Carlo sampling methods using Markov chains and their applications (1970)
  10. An introduction to \uppercase MCMC for machine learning (2003)
  11. Equation of state calculations by fast computing machines (1953)
  12. The monte carlo method (1949)
  13. The metropolis algorithm (2000)
  14. Techniques for estimating the bit error rate in the simulation of digital communication systems (1984)
  15. Markov chain Monte Carlo in practice (1995)
  16. Ensemble Kalman filter based Sequential Monte Carlo Sampler for sequential Bayesian inference (2020) — link
  17. Basics of applied stochastic processes (2009)
  18. Bayesian data analysis (2013)
  19. System Reliability and Risk Analysis by Monte Carlo Simulation (2013)
  20. The beginning of the Monte Carlo method (1987)
  21. Importance sampling for portfolio credit risk (2005)
  22. From Cardinals to Chaos: Reflections on the Life and Legacy of \uppercase S tanislaw \uppercase U lam (1989)
  23. The probability, identification, and prevention of rare events in power systems (2004)
  24. Tables for testing the goodness of fit of theory to observation (1902)
  25. An efficient surrogate-based method for computing rare failure probability (2011)
  26. Advanced probabilistic structural analysis method for implicit performance functions (1990)
  27. Theory of ground vehicles (2008)
  28. Rare event simulation using Monte Carlo methods (2009)
  29. Hamiltonian Monte Carlo methods for subset simulation in reliability analysis (2019)
  30. Estimation of small failure probability using generalized subset simulation (2022)
  31. A refined subset simulation for the reliability analysis using the subset control variate (2020)
  32. Time-variant system reliability analysis method for a small failure probability problem (2021)
  33. An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability (2019)
  34. \uppercase AK-MSS : An adaptation of the \uppercase AK-MCS method for small failure probabilities (2020)
  35. A coupled subset simulation and active learning kriging reliability analysis method for rare failure events (2019)
  36. Bayesian subset simulation (2017)
  37. Estimation of small failure probabilities in high dimensions by subset simulation (2001)
  38. Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions (2012)
  39. Reliability-based design optimization using kriging surrogates and subset simulation (2011)
  40. \uppercase MCMC algorithms for subset simulation (2015)
  41. Assessing small failure probabilities by combined subset simulation and support vector machines (2011)
  42. Application of subset simulation methods to reliability benchmark problems (2007)
  43. Subset simulation method for rare event estimation: an introduction (2015) — link
  44. Multicanonical ensemble: A new approach to simulate first-order phase transitions (1992)
  45. Multicanonical algorithms for first order phase transitions (1991)
  46. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling (1977)
  47. Introduction to multicanonical Monte Carlo simulations (2000)
  48. Multicanonical communication system modeling-application to \uppercase PMD statistics (2002)
  49. Error estimation in multicanonical Monte Carlo simulations with applications to polarization-mode-dispersion emulators (2005)
  50. Multicanonical MCMC for sampling rare events: an illustrative review (2014)
  51. A subset multicanonical Monte Carlo method for simulating rare failure events (2017)
  52. Accelerating sequential Monte Carlo with surrogate likelihoods (2021)
  53. Controlled sequential monte carlo (2020)
  54. Comparison of resampling schemes for particle filtering (2005)
  55. Increasing the efficiency of Sequential Monte Carlo samplers through the use of approximately optimal L-kernels (2022)
  56. An invitation to sequential Monte Carlo samplers (2020) — link
  57. Sequential monte carlo samplers with independent markov chain monte carlo proposals (2019)
  58. Nested sequential monte carlo methods (2015)
  59. A critical appraisal of reliability estimation procedures for high dimensions (2004)
  60. A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification (2016)
  61. Portfolio credit risk with extremal dependence: Asymptotic analysis and efficient simulation (2008)
  62. Rare-event probability estimation with conditional Monte Carlo (2011)
  63. A discussion on recent risk measures with application to credit risk: Calculating risk contributions and identifying risk concentrations (2018)
  64. On default correlation: A copula function approach (2000)
  65. Creditmetrics-technical document (1997)
  66. Uncertainty quantification: theory, implementation, and applications (2013)
  67. Stochastic Processes with Applications to Finance. (1957)
  68. Lectures on probability theory and mathematical statistics (2017)
  69. Statistical thought: a perspective and history (2003)
  70. M 'e moire sur la probabilit 'e de causes par les 'e venements (1774)
  71. An essay towards solving a problem in the doctrine of chances. (1763)
  72. Fundamentals of investments (2001)
  73. Failing to forecast rare events (2021)
  74. Measuring market risk (2007)
  75. Options, futures and other derivatives (2019)
  76. Stochastic processes with applications to finance (2016)
  77. Markov chain monte carlo methods for estimating systemic risk allocations (2020)
  78. Valuing American options by simulation: a simple least-squares approach (2001)
  79. Sharp asymptotics for large portfolio losses under extreme risks (2019)
  80. Population monte carlo (2004)
  81. Rare Events via Cross-Entropy Population Monte Carlo (2021)
  82. Population Monte Carlo Path Tracing (2007)
  83. Population Monte Carlo algorithm in high dimensions (2011)
  84. An overview of existing methods and recent advances in sequential Monte Carlo (2007)
  85. Minimum variance importance sampling via population Monte Carlo (2007)
  86. Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems (2003)
  87. Importance sampling for polarization-mode dispersion (2002)
  88. On the stability of sequential Monte Carlo methods in high dimensions (2014)
  89. Application of line sampling simulation method to reliability benchmark problems (2007)
  90. Reliability of structures in high dimensions, part I: algorithms and applications (2004)
  91. Evaluation of failure probability via surrogate models (2010)
  92. Accelerating asymptotically exact \uppercase MCMC for computationally intensive models via local approximations (2016)
  93. The cross-entropy method for combinatorial and continuous optimization (1999)
  94. A tutorial on the cross-entropy method (2005)
  95. Monte Carlo methods in financial engineering (2004)
  96. A review of copula models for economic time series (2012)
  97. A general procedure for first/second-order reliability method (FORM/SORM) (1999)
  98. Rare-event simulation techniques: an introduction and recent advances (2006)
  99. Modelling dependent defaults (2001)
  100. Modelling dependence with copulas (2001)
  101. Beyond correlation: Extreme co-movements between financial assets (2002)
  102. Estimation methods for expected shortfall (2014)
  103. Efficient estimation of large portfolio loss probabilities in t-copula models (2010)
  104. Monte Carlo methods for value-at-risk and conditional value-at-risk: a review (2014)
  105. Coherent measures of risk (1999)
  106. Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms (1994)
  107. Methods of reducing sample size in Monte Carlo computations (1953)
  108. Structural causes of the global financial crisis: a critical assessment of the `new financial architecture’ (2009)
  109. Global financial stability report (2009)
  110. Time series analysis and its applications (2000)
  111. Analysis of financial time series (2005)
  112. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation (1982)
  113. Multicanonical Monte-Carlo simulations of light propagation in biological media (2005)
  114. Markov Chain Monte Carlo Simulations and Their Statistical Analysis: With Web-based Fortran Code (2004)
  115. A guide to Monte Carlo simulations in statistical physics (2014)
  116. Searching for rare growth factors using multicanonical Monte Carlo methods (2007)
  117. A nonparametric estimation of the entropy for absolutely continuous distributions (corresp.) (1976)
  118. Applied groundwater modeling: simulation of flow and advective transport (1992)
  119. Estimation of small failure probabilities in high dimensions by subset simulation (2001)
  120. A new adaptive importance sampling scheme for reliability calculations (1999)
  121. Kriging-based adaptive importance sampling algorithms for rare event estimation (2013)
  122. Sequential design of computer experiments for the estimation of a probability of failure (2012)
  123. Nonparametric entropy estimation: An overview (1997)
  124. Efficient global reliability analysis for nonlinear implicit performance functions (2008)
  125. Probability integration by directional simulation (1988)
  126. Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization (2007)
  127. A fast and efficient response surface approach for structural reliability problems (1990)
  128. Sequential Monte Carlo for rare event estimation (2012)
  129. Refined second-order reliability analysis (1994)
  130. Free energy methods for Bayesian inference: efficient exploration of univariate Gaussian mixture posteriors (2012)
  131. Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations (2014) — link
  132. A tutorial on cross-entropy method (2005)
  133. Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004) — link
  134. Efficient algorithm for second-order reliability analysis (1991)
  135. Second-order reliability approximations (1987)
  136. Second-Order Reliability Approximations (1987) — link
  137. Methods of structural systems reliability (1986)
  138. Structural Reliability Methods (2007)
  139. Structural reliability methods (1996)
  140. Sequential optimization and reliability assessment method for efficient probabilistic design (2004)
  141. Metamodel-based importance sampling for structural reliability analysis (2013)
  142. AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation (2011)
  143. A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013)
  144. A benchmark study on importance sampling techniques in structural reliability (1993)
  145. Response surface approach for reliability analysis (1989)
  146. Quadratic limit states in structural reliability (1979)
  147. CQ2RS : a new statistical approach to the response surface method for reliability analysis (2003)
  148. SOA intensity noise suppression in spectrum sliced systems: A multicanonical Monte Carlo simulator of extremely low BER (2009)
  149. Higher-order failure probability calculation using nonlinear approximations (1999) — [link](https://doi.org/DOI: 10.1016/S0045-7825(98)00140-6)
  150. Reliability-based structural optimization using improved two-point adaptive nonlinear approximations (1998) — [link](https://doi.org/DOI: 10.1016/S0168-874X(98)00007-9)
  151. An improved response surface method for the determination of failure probability and importance measures (2004)
  152. On the estimation of entropy (1993)
  153. A framework for decision-based engineering design (1998)
  154. New light on first- and second-order reliability methods (1987)
  155. Improvement of second-order reliability estimates by importance sampling (1988)
  156. First-order concepts in system reliability (1983)
  157. A Study on the Cross-Entropy Method for Rare-Event Probability Estimation (2007)
  158. Simulation-based optimal Bayesian experimental design for nonlinear systems (2013) — link
  159. Estimation of entropy and other functionals of a multivariate density (1989)
  160. Uncertainty propagation in CFD using polynomial chaos decomposition (2006) — link
  161. Reliability of structures in high dimensions, part I : algorithms and applications (2004)
  162. New approximations for SORM integrals (1994)
  163. Near-Optimal Sensor Placements in Gaussian Processes-Theory, Efficient Algorithms and Empirical Studies (2008) — link
  164. Evaluation of failure probability via surrogate models (2010)
  165. Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure (2012) — link
  166. A polynomial chaos approach to measurement uncertainty (2006) — link
  167. Finite mixture models (2004)
  168. Structural system reliability assessment using directional simulation (1994)
  169. Importance sampling in structural systems (1989)
  170. Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method (2005)
  171. Directional methods for structural reliability (2000)
  172. Curve fitting and optimal design for prediction (1978)
  173. Kriging: a method of interpolation for geographical information systems (1990)
  174. A study using Monte Carlo Simulation for failure probability calculation in Reliability-Based Optimization (2006)
  175. Adapted polynomial chaos expansion for failure detection (2007) — [link](https://doi.org/DOI: 10.1016/j.jcp.2007.04.011)
  176. Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems (2010)
  177. Reliability analysis – a review and some perspectives (2001)
  178. Reliability analysis—a review and some perspectives (2001)
  179. A new look at the response surface approach for reliability analysis (1993)
  180. Optimization of conditional value-at-risk (2000)
  181. Optimization of computer simulation models with rare events (1997)
  182. Simulation and the Monte Carlo method (2007)
  183. The cross-entropy method (2004)
  184. A critical appraisal of reliability estimation procedures for high dimensions (2004)
  185. A critical appraisal of methods to determine failure probabilities (1987)
  186. Autocrine loops with positive feedback enable context-dependent cell signaling (2002) — link
  187. Kriging models for global approximation in simulation-based multidisciplinary design optimization (2001)
  188. Implementation of the simultaneous perturbation algorithm for stochastic optimization (1998)
  189. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation (1992)
  190. Global sensitivity analysis using polynomial chaos expansions (2008) — [link](https://doi.org/DOI: 10.1016/j.ress.2007.04.002)
  191. Gaussian processes for machine learning (2006)
  192. Slope reliability and response surface method (1985)
  193. A general procedure for first/second-order reliability method ( FORM/SORM ) (1999)
  194. Computing failure probabilities. Applications to reliability analysis (2002) — [link](https://doi.org/DOI: 10.1016/S0951-8320(02)00037-6)
  195. MCMC Using Hamiltonian Dynamics (2011)
  196. Multilevel sequential monte carlo samplers (2017)
  197. A surrogate accelerated multicanonical monte carlo method for uncertainty quantication (2016)
  198. Parallel markov chain monte carlo (2013) — link
  199. Parallelizing MCMC sampling via space partitioning (2022)
  200. Global failure probability function estimation based on an adaptive strategy and combination algorithm (2023)
  201. An enhanced method for improving the accuracy of small failure probability of structures (2022)
  202. An adaptive parallel learning dependent Kriging model for small failure probability problems (2022)
  203. Reliability based design optimization with approximate failure probability function in partitioned design space (2017)
  204. A review and assessment of importance sampling methods for reliability analysis (2022)
  205. Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation (2021)
  206. A conceptual introduction to Hamiltonian Monte Carlo (2017) — link
  207. The geometry of limit state function graphs and subset simulation: Counterexamples (2019)
  208. Design optimization using subset simulation algorithm (2010)
  209. An application of swarm optimization to nonlinear programming (2005)
  210. Portfolio optimization with entropic value-at-risk (2019)
  211. Liquidity-adjusted value-at-risk optimization of a multi-asset portfolio using a vine copula approach (2019)
  212. Benchmark study of numerical methods for reliability-based design optimization (2010)
  213. Value-at-risk in portfolio optimization: properties and computational approach (2005)
  214. Worst-case value-at-risk and robust portfolio optimization: A conic programming approach (2003)
  215. A global optimization heuristic for portfolio choice with VaR and expected shortfall (2002)
  216. A data-driven optimization heuristic for downside risk minimization (2006)
  217. An evolutionary computation approach to scenario-based risk-return portfolio optimization for general risk measures (2007)
  218. 60 Years of portfolio optimization: Practical challenges and current trends (2014)
  219. Portfolio optimization with conditional value-at-risk objective and constraints (2002)
  220. Portfolio Selection (1952)
  221. Beyond VaR: from measuring risk to managing risk (1999)
  222. VaR is a dangerous technique (1996)
  223. A cross-entropy method for value-at-risk constrained optimization (2011)
  224. Optimizing conditional Value-At-Risk of black-box functions (2021)
  225. Portfolio optimization under the value-at-risk constraint (2007)
  226. Value-at-risk vs. conditional value-at-risk in risk management and optimization (2008)
  227. Value-at-risk optimization using the difference of convex algorithm (2012)
  228. Entropic value-at-risk: A new coherent risk measure (2012)
  229. Liquidity adjusted value-at-risk based on the components of the bid-ask spread (2006)
  230. Robustness in the optimization of risk measures (2022)
  231. Stochastic subset optimization for optimal reliability problems (2008)
  232. An efficient framework for optimal robust stochastic system design using stochastic simulation (2008)
  233. Neural-progressive hedging: Enforcing constraints in reinforcement learning with stochastic programming (2022)
  234. Bayesian quantile and expectile optimisation (2022)
  235. Trieste (2023) — link
  236. 229Optimization Under Unknown Constraints (2011) — link
  237. Bayesian optimization under uncertainty (2017)
  238. Bayesian optimization with inequality constraints. (2014)
  239. Bayesian optimization with unknown constraints (2014) — link
  240. A taxonomy of global optimization methods based on response surfaces (2001)
  241. Efficient global optimization of expensive black-box functions (1998)
  242. On Bayesian methods for seeking the extremum (1975)
  243. Slice sampling covariance hyperparameters of latent Gaussian models (2010)
  244. Value-at-risk optimization with Gaussian processes (2021)
  245. Gaussian processes in machine learning (2003)
  246. Practical bayesian optimization of machine learning algorithms (2012)
  247. Maximizing acquisition functions for Bayesian optimization (2018)
  248. Kriging is well-suited to parallelize optimization (2010)
  249. Optimizing the CVaR via sampling (2015)
  250. Differential evolution with DEoptim: an application to non-convex portfolio optimization (2011)
  251. Minimizing CVaR and VaR for a portfolio of derivatives (2006)
  252. Honest exploration of intractable probability distributions via Markov chain Monte Carlo (2001)
  253. Benchmark study on reliability estimation in higher dimensions of structural systems–an overview (2007)
  254. Worst-case value at risk of nonlinear portfolios (2013)
  255. Portfolio Allocation for Bayesian Optimization. (2011)
  256. Bayesian optimization of risk measures (2020)
  257. Bayesian optimization with expensive integrands (2018) — link
  258. Robust multi-objective bayesian optimization under input noise (2022)
  259. Scalable constrained Bayesian optimization (2021)
  260. Constrained Bayesian optimization with noisy experiments (2019)
  261. Lookahead Bayesian optimization with inequality constraints (2017)
  262. On provably robust meta-Bayesian optimization (2022)
  263. Multi-objective bayesian optimization over high-dimensional search spaces (2022)
  264. Efficient rollout strategies for Bayesian optimization (2020)
  265. Modeling an augmented Lagrangian for blackbox constrained optimization (2016)
  266. Bayesian Optimization for Cascade-Type Multistage Processes (2022)
  267. Noisy-input entropy search for efficient robust Bayesian optimization (2020)
  268. Investments. international edition (2002)
  269. Bayesian Neural Networks for Financial Asset Forecasting (2019)
  270. Efficient capital markets: A review of theory and empirical work (1970)
  271. Real-time prediction and post-mortem analysis of the Shanghai 2015 stock market bubble and crash (2015)
  272. Lag order and critical values of the augmented Dickey–Fuller test (1995)
  273. On a measure of lack of fit in time series models (1978)
  274. Generalized autoregressive conditional heteroskedasticity (1986)
  275. Corporate finance (2007)
  276. The black swan: Why don’t we learn that we don’t learn (2005)
  277. The effect of COVID-19 pandemic on global stock markets: Return, volatility, and bad state probability dynamics (2022)
  278. BP deepwater horizon costs Balloon to 65 billion (2018) — link
  279. Consequences of the war in ukraine the economic fallout (2023) — link
  280. The global financial crisis: Causes and consequences (2010)
  281. Russia’s Invasion of Ukraine and Its Impact on Stock Prices (2022) — link
  282. How does the war in Ukraine affect oil prices? (2022) — link
  283. Oil market has fully absorbed impact of Russia’s invasion of Ukraine (2022) — link
  284. Elements of financial risk management (2011)
  285. Value at risk and expected stock returns (2004)
  286. Value at risk, cross-sectional returns and the role of investor sentiment (2020)
  287. Empirical analysis of the intertemporal relationship between downside risk and expected returns: Evidence from time-varying transition probability models (2016)
  288. Some remarks on the value-at-risk and the conditional value-at-risk (2000)
  289. Predictive ability of Value-at-Risk methods: evidence from the Karachi Stock Exchange-100 Index (2010)
  290. Value at Risk: The New Benchmark for Managing Financial Risk (2000)
  291. RiskMetrics - Technical Document (1996)
  292. RiskMetrics Value-at-Risk: Theory and practice (2016) — link
  293. Value at Risk — link
  294. Marginal likelihood computation for model selection and hypothesis testing: an extensive review (2023)
  295. Simulating ratios of normalizing constants via a simple identity: A theoretical exploration (1996)
  296. Slice sampling (2003)
  297. Replica Monte Carlo Simulation of Spin-Glasses (1986)
  298. Computing Bayes factors using thermodynamic integration (2006)
  299. Improving Marginal Likelihood Estimation for Bayesian Phylogenetic Model Selection (2010)
  300. Annealed importance sampling (2001)
  301. Nested Sampling for General Bayesian Computation (2006)
  302. Uncertainty Quantification
  303. Uncertainty Quantification
  304. Into the Unknown: Uncertainty, Foreboding and Financial Markets
  305. Rare Events and Financial Markets
  306. Measurement of Extreme Market Risk: Insights from a Full Article
  307. Extreme Value Dependence in Financial Markets: Diagnostics
  308. An Efficient Rare Event Simulation-Based Methodology for Pricing
  309. Efficient black-box importance sampling for VaR and CVaR estimation (2021)
  310. Variance reduction for risk measures with importance sampling in nested simulation (2022) — link
  311. The Application of Bayesian Methods for Seeking the Extremum (1978)
  312. Practical Bayesian Optimization (2008)
  313. Gaussian Processes for Regression and Optimisation (2007)
  314. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning (2010) — link
  315. Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning (2020) — link
  316. Structural reliability methods (1996)
  317. New light on first- and second-order reliability methods (1987)
  318. Asymptotic approximations for multinormal integrals (1984)
  319. The New International Regulation of Market Risk: Roles of VaR and CVaR in Model Validation (2021)
  320. Conditional-value-at-risk estimation via reduced-order models (2018)
  321. Time Series Analysis: Forecasting and Control (2015)
  322. Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances (1992)
  323. Bayesian econometrics (2001)
  324. Bayesian Forecasting and Dynamic Models (2006)
  325. Asymptotic properties of the maximum likelihood estimators and likelihood ratio tests under nonstandard conditions (2003)
  326. A forecast comparison of volatility models: does anything beat a GARCH(1,1)? (2005)
  327. Detection of rare events: A machine learning toolkit with an application to banking crises (2019)
  328. A machine-learning-based importance sampling method to compute rare event probabilities (2020)
  329. Understanding the differences between Bayesian and frequentist statistics (2022)
  330. Evaluation of forecasting methods from selected stock market returns (2019)
  331. A general framework of importance sampling for value-at-risk and conditional value-at-risk (2009)
  332. A comprehensive review of deterministic models and applications for mean-variance portfolio optimization (2019)
  333. Robust portfolio optimization: a categorized bibliographic review (2020)
  334. Prospect Theory: An Analysis of Decision under Risk (1979)
  335. The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution (2019)
  336. 80% of the stock market is now on autopilot (2019) — link
  337. Buffett’s Alpha (2018)
  338. A behavioral approach to asset pricing (2008)
  339. The Misbehavior of Markets: A fractal view of financial turbulence (2007)
  340. Irrational exuberance (2015)
  341. Irving Fisher and Financial Economics: The Equity Premium Puzzle, the Predictability of Stock Prices, and Intertemporal Allocation Under Risk (2007) — link
  342. Regression and time series model selection (1999)
  343. Market timing and return prediction under model instability (2001)
  344. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  345. Handbook of heavy tailed distributions in finance (2003)
  346. Bayesian analysis of ARMA–GARCH models: A Markov chain sampling approach (2000)
  347. Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo (2021)
  348. Modern portfolio theory and behavioral finance (2004)
  349. Russia’s Invasion of Ukraine and Its Impact on Stock Prices (2022) — link
  350. Estimation of failure probabilities in the presence of competing risks: new representations of old estimators (1999)
  351. Recipe for Disaster: The Formula That Killed Wall Street (2009) — link
  352. Conditional value-at-risk for general loss distributions (2002)
  353. Correlation and dependence in risk management: properties and pitfalls (2002)
  354. Modelling Extremal Events: for Insurance and Finance (2013)
  355. Quantitative Risk Management: Concepts, Techniques and Tools (2015)
  356. The Fed caused 93% of the entire stock market’s move since 2008: Analysis (2016) — link
  357. Radical Uncertainty: Decision-Making for an Unknowable Future (2020)
  358. The General Theory of Employment, Interest, and Money (1936)
  359. Market Models: A Guide to Financial Data Analysis (2008)
  360. Risk management and financial institutions,+ Web Site (2012)
  361. Surrogate-based methods (2011)
  362. Multicanonical sequential Monte Carlo sampler for uncertainty quantification (2023)
  363. Nobel lecture: Uncertainty outside and inside economic models (2014)
  364. Uncertainty outside and inside economic models (2013)
  365. Tail risk and asset prices (2014)
  366. A Treatise on Probability (1921)
  367. Risk, Uncertainty, and Profit (1921)
  368. Robust Control and Model Uncertainty (2001)
  369. Recursive Robust Estimation and Control Without Commitment (2007)
  370. Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions (2003)
  371. Asymptotic Efficiency in Estimation with Conditional Moment Restrictions (1987)
  372. Efficient Instrumental Variables Estimation of Nonlinear Models (1990)
  373. Ambiguity, Risk, and Asset Returns in Continuous Time (2002)
  374. Understanding uncertainty shocks and the role of black swans (2014)
  375. A Theory of Asset Pricing Based on Heterogeneous Information (2015)
  376. Tail Risk Concerns Everywhere (2018)
  377. Tail Risk and Asset Prices (2014)
  378. On Existence and Uniqueness of Equilibrium in a Class of Noisy Rational Expectations Models (2015)
  379. Endogenous Uncertainty and Credit Crunches (2021)
  380. Multi-Asset Noisy Rational Expectations Equilibrium with Contingent Claims (2021)
  381. The Conquest of US Inflation: Learning and Robustness to Model Uncertainty (2005)
  382. Various Works on Tail Risk in Asset Pricing and Business Cycle Fluctuations (1988, 2006, 2013)
  383. Policy Uncertainty Index (2015)
  384. A simple test for heteroskedasticity and random coefficient variation (1979)
  385. Gaussian processes for machine learning (2006)
  386. The theory of stock market efficiency: accomplishments and limitations (1996)
  387. Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk (2019)

0 of 395 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.