# A stock model with jumps for Itô–Liu financial markets

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## Abstract

Over the years, various types of differential equations have been employed to describe a myriad of processes driven by the respective forms of indeterminacy. This paper presents and examines uncertain stochastic differential equations and their important characteristics. An uncertain stochastic differential equation is a differential equation driven by both a Brownian motion and a canonical Liu process. Moreover, an uncertain stochastic differential equation with jumps is a differential equation driven by a Brownian motion, a canonical Liu process and an uncertain random renewal process. Based on an uncertain stochastic differential equation with jumps, this study suggests a stock model with jumps for Itô–Liu financial markets. Generalised stock models for Itô–Liu financial markets are introduced as well.

## Keywords

Indeterminacy Uncertain stochastic differential equation Uncertain stochastic differential equation with jumps Uncertain stochastic finance Stock model with jumps Itô–Liu financial markets## Notes

### Acknowledgements

The authors would like to express their heartfelt gratitude towards the Great Zimbabwe University (Department of Mathematics and Computer Science and Department of Banking and Finance) for providing excellent research support and facilities.

### Author Contributions

Both authors contributed to the generation of this research article. The authors read and approved the final manuscript.

### Compliance with ethical standards

### Conflict of interest

The authors hereby declare that they have no conflict of interest.

### Ethical approval

The article does not contain any studies with human participants or animals performed by any of the authors.

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