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We develop a new split-step θ (SS θ ) method for stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the SS θ method for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory.

Strong Convergence of the Split-Step θ -Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes