In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are ideally suited for an integration of various types of probabilistic constraints. We show an approach on how to integrate these constraints. Numerical results u...

We implement the recently introduced Poisson approximation on a density dependent jump process corresponding to a simple, but not exactly solvable, epidemiological model. Statistics produced with 10 independent realizations of the Feller process are compared with equivalent statistics produced with Poisson, proper Gaussian and diffusion realizations. While in the Poisson approximation the stati...

In this paper, we investigate pollutant reduction policies under uncertainty. We assume that when an agent reduces quantity of a pollutant, it incurs costs. We consider two kinds of policies distinguished by their costs. One policy incurs proportional reduction cost (Case 1) and the other incurs fixed and proportional reduction costs (Case 2). To solve these problems, we formulate the agent’s p...

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection–pursuit with different smoothing methods. Consistency of the estimators are shown u...

in this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. the filtering problem have animportant role in the theory of stochastic differential equations(sdes). in thisarticle, we present an application of the continuous kalman-bucy filter for a rlcircuit. the deterministic model of the circuit is replaced by a stochastic model byadding a ...

Recently time-reversal techniques have emerged as a new, important and fascinating discipline within wave propagation. Many of the problems involved can best be understood, analysed and optimized based on a random field model for the medium. Here we discuss stable refocusing of second-order time-reversed reflections. This phenomenon may appear as surprising at first. However, we show how it can...

In this paper we deal with the numerical approximation of integro-differential equations arising in financial applications in which jump processes act as the underlying stochastic processes. Our aim is to find finite differences schemes which are high-order accurate for large time regimes. Therefore, we study the asymptotic time behavior of such equations and we define as asymptotic high-order ...

This course introduces main concepts from the theory of random sets with emphasis on applications in economics and finance: most importantly inference for partially identified models and transaction costs modelling. The main mathematical ideas introduced in this course are that of a random closed set, its distribution and main analytical tools to handle it, selections and expectations of random...

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of prob...

We provide a detailed derivation of the Karhunen-Loève expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.