Related papers: Bayesian Uncertainty Quantification of Local Volat…

Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…

Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…

Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural…

Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…

We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…

The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict…

We develop a Bayesian framework for the efficient estimation of impulse responses using Local Projections (LPs) with instrumental variables. It accommodates multiple shocks and instruments, accounts for autocorrelation in multi-step…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…

In this paper, we describe a general method for constructing the posterior distribution of an option price. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…