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This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE…
In a discrete time stochastic model of a pension investment funds market Gajek and Kaluszka(2000a) have provided a definition of the average rate of return which satisfies a set of economic correctnes postulates. In this paper the average…
This study seeks to advance the understanding and prediction of stock market return uncertainty through the application of advanced deep learning techniques. We introduce a novel deep learning model that utilizes a Gaussian mixture…
Long-term investors, different from short-term traders, focus on examining the underlying forces that affect the well-being of a company. They rely on fundamental analysis which attempts to measure the intrinsic value an equity.…
\noindent Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental and ecological applications. In this paper, we investigate…
Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
This paper presents a new method to assess default risk based on applying the CEV process to the KMV model. We find that the volatility of the firm asset value may not be a constant, so we assume the firm's asset value dynamics are given by…
An insurance company is required to prepare a certain amount of money, called reserve, as a mean to pay its policy holders claims in the future. There are several types of reserve, one of them is IBNR reserve, for which the payments are…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for discriminative training of probabilistic generative models belonging to the exponential family. In this work, we introduce and justify this algorithm as a stochastic…