On stochastic integrals with controlled growth of their containing range

TL;DR

This paper introduces specific examples of stochastic Ito integrals with bounded growth of their range, providing explicit integrands without relying on stopping times or conditional expectation calculations.

Contribution

It presents explicit constructions of stochastic Ito integrals with controlled growth, avoiding the use of stopping times and conditional expectations.

Findings

Explicit integrands with controlled growth are constructed.

The approach simplifies the analysis of stochastic integrals.

No stopping times or conditional expectations are needed.

Abstract

This short note suggests special examples of stochastic Ito integrals with controlled growth of their containing range. The integrands for this integrals are presented explicitly. The construction does not involve neither stopping times nor forecasting or calculation of the conditional expectations of a contingent claim