Jump diffusion geometric Brownian motion with the re-invested dividend yielding asset and transaction cost
Author(s): Mark Opondo, Francis Odundo and Daniel Brian Oduor
Abstract: We consider an investment model where surplus
evolves under a jump diffusion risk process. The financial institution
reinvests proportional dividends and allocates surplus between a risk-free
asset and a risky asset whose return follows a jump diffusion process. While
jump diffusion models capture discontinuities in asset pricing, they often have
limitations. To enhance realism, we model the risky asset’s price using a
Brownian motion risk model incorporating dividends and transaction costs, where
the instantaneous investment return follows a Geometric Brownian motion with
jump diffusion. Applying Itô’s lemma, we derive the asset price for this
framework, accounting for reinvested dividends and transaction costs.
Mark Opondo, Francis Odundo, Daniel Brian Oduor. Jump diffusion geometric Brownian motion with the re-invested dividend yielding asset and transaction cost. Int J Stat Appl Math 2025;10(4):46-53. DOI: 10.22271/maths.2025.v10.i4a.2022
