Optimal importance sampling for Lévy processes
نویسندگان
چکیده
منابع مشابه
Optimal Importance Sampling Parameter Search for Lévy Processes via Stochastic Approximation
The author proposes stochastic approximation methods of finding the optimal measure change by the exponential tilting for Lévy processes in Monte Carlo importance sampling variance reduction. In accordance with the structure of the underlying Lévy measure, either a constrained or unconstrained algorithm of the stochastic approximation is chosen. For both cases, the almost sure convergence to a ...
متن کاملOptimal portfolios for exponential Lévy processes
We consider the problem of maximizing the expected utility from consumption or terminal wealth in a market where logarithmic securities prices follow a Lévy process. More specifically, we give explicit solutions for power, logarithmic and exponential utility in terms of the Lévy-Chinchine triplet. In the first two cases, a constant fraction of current wealth should be invested in each of the se...
متن کاملImportance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes
This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by ...
متن کاملAn importance sampling method based on the density transformation of Lévy processes
In this paper, we develop an importance sampling method with the help of flexible control on the Lévy measure in the density transformation. The method has significant efficacy even on evaluating random variables with complex path-dependent structures. Numerical examples are presented to illustrate convergence acceleration through variance reduction with a view towards financial derivatives pri...
متن کاملOptimal stopping and perpetual options for Lévy processes
Consider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options involving the infimum of the after-mentioned process are obtained. As a direct application of the previou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2020
ISSN: 0304-4149
DOI: 10.1016/j.spa.2018.12.019