Related papers: Local risk-minimization for exponential additive p…
This paper presents a comprehensive algorithm for fitting generative models whose likelihood, moments, and other quantities typically used for inference are not analytically or numerically tractable. The proposed method aims to provide a…
For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L\'evy measure of the inverse local time is subexponential…
Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often…
A dynamical model consists of a continuous self-map $T: \mathcal{X} \to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f: \mathcal{X} \to \mathbb{R}$. This paper considers the fitting of a…
Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are…
This paper proposes additional material to the main statements of [HL13] which are are recalled in Section~2. In particular an application of [Theorem~2.2,HL13] to Renewal Markov Processes is provided in Section~4 and a detailed checking of…
We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential L\'evy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
In many estimation problems, e.g. linear and logistic regression, we wish to minimize an unknown objective given only unbiased samples of the objective function. Furthermore, we aim to achieve this using as few samples as possible. In the…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure $P$ and corresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$ respectively. Then, we…
Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a…
This paper considers an empirical risk minimization problem under heavy-tailed settings, where data does not have finite variance, but only has $p$-th moment with $p \in (1,2)$. Instead of using estimation procedure based on truncated…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility…
In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…
Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie…
We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit…