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Journal of Applied Mathematics and Computation

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Article Open Access http://dx.doi.org/10.26855/jamc.2025.06.004

Locally Risk-Minimising (LRM) Strategy with Jumps in Both Bond and Risky Assets

W. Nangolo*, R. B. Gnitchogna

Department of Computing, Mathematical & Statistical Science, University of Namibia, Windhoek 13301, Namibia.

*Corresponding author:W. Nangolo

Published: June 17,2025

Abstract

Uncertainty quantification (UQ) has become an indispensable component of regulatory and risk management frameworks. The financial literature increasingly emphasizes the imperative of mandatory implementation of UQs, especially in the valuation and hedging of financial derivatives. This study proposes a locally risk-minimizing (LRM) strategy with a jump process into the stochastic differential equations, both in the bond asset and in the risky asset. The aim is to account, respectively, for shifts or distortions in the yield curve, as seen with the COVID-19 pandemic, and for the undiversifiable derivatives market’s volatility. The LRM strategy as a robust hedging approach facilitates UQ within the context of derivative markets. We focus on incomplete market models, where LRM strategies are designed to minimize the variance of the underlying asset(s) at a given time t, while ensuring that the portfolio replicates the desired payoff at maturity T. The aim is to provide more accurate and efficient approximations of uncertainty quantities associated with financial derivatives.

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How to cite this paper

Locally Risk-Minimising (LRM) Strategy with Jumps in Both Bond and Risky Assets

How to cite this paper: W. Nangolo, R. B. Gnitchogna. (2025) Locally Risk-Minimising (LRM) Strategy with Jumps in Both Bond and Risky Assets. Journal of Applied Mathematics and Computation9(2), 120-135.

DOI: http://dx.doi.org/10.26855/jamc.2025.06.004