In this paper, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem with model uncertainty. We introduce a generalized infinitesimal perturbation analysis (IPA) approach to resolve the difficulty caused by discontinuity of the optimal decision with resp...

Interpretation with Infinitesimals ? Towards Scalability in Nonstandard Static Analysis Kengo Kido, Swarat Chaudhuri, and Ichiro Hasuo 1 University of Tokyo, Japan 2 JSPS Research Fellow 3 Rice University, USA Abstract. We extend abstract interpretation for the purpose of verifying hybrid systems. Abstraction has been playing an important role in many verification methodologies for hybrid syste...

Image analysis methods that use histograms defined over non-zero-sized local neighbourhoods have been proposed [1-4]. To better understand such methods, one can study the histograms of infinitesimal neighbourhoods. In this paper we show how the properties of such histograms can be derived through limit arguments. We show that in many cases the properties of these histograms are given by simple ...

Comparison of the oscillatory behavior of a gravitating infinite Nambu-Goto string and a test string is investigated using the general relativistic gauge invariant perturbation technique with two infinitesimal parameters on a flat spacetime background. Due to the existence of the pp-wave exact solution, we see that the conclusion that the dynamical degree of freedom of an infinite Nambu-Goto st...