相关论文: Skewness Premium with L\'evy Processes

Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of…

We study the small-time asymptotics of sample paths of L\'evy processes and L\'evy-type processes. Namely, we investigate under which conditions the limit $$\limsup_{t \to 0} \frac{1}{f(t)} |X_t-X_0|$$ is finite resp.\ infinite with…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

This paper studies de Finetti's optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a L\'evy process that may have positive and negative jumps. The…

In this article, we study the asymptotic behaviour of L\'evy processes with no positive jumps conditioned to stay positive. We establish integral tests for the lower envelope at 0 and at $+\infty$ and an analogue of Khintchin's law of the…

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…

The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…

Given a discrete time sample $X_1,... X_n$ from a L\'evy process $X=(X_t)_{t\geq 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\gamma,\sigma^2,\rho)$ corresponding to the…

We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose…

We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…

We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…

The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential L\'evy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of…

We introduce a class of L\'{e}vy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions…

Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…

In this article we get simple explicit formulas for $\Exp\sup_{s\leq t}X(s)$ where $X$ is a spectrally positive or negative L\'evy process with infinite variation. As a consequence we derive a generalization of the well-known formula for…

For a spectrally negative L\'evy process $X$, we study the following distribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t \mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \mathrm{d}y \right], $$ where $-\infty \leq a < b < \infty$,…

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine…

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…

The notion of a homogeneous standard filtration of $\sigma$-algebras was introduced by the author in 1970. The main theorem asserted that a homogeneous filtration is standard, i.e., generated by a sequence of independent random variables,…