Abstract
Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of stochastic age-dependent capital systems with Poisson jumps and fractional Brownian motion (fBm) and investigate the convergence of the split-step θ-method (SSθ) for this system. It is proved that the numerical approximation solutions converge to the analytic solutions for the equations, and the order of approximation is also provided. Finally, a numerical experiment is simulated to illustrate that the SSθ method has better accuracy than the Euler method.
Highlights
For the past few years, stochastic age-dependent capital systems have become increasingly important mathematical tools to portray many financial phenomena in the real world
Zhang et al [1] discussed the exponential stability of Euler approximation for the stochastic age-dependent capital system with Poisson jumps, and further studied the convergence of Euler method for a class of stochastic age-dependent capital systems with random jump magnitudes and Markovian switching [2, 3]
It is easy to verify that the maximum value of the error square for the split-step θ -method (SSθ) approximation is not greater than 0.01, which is smaller than the error of the EM method [3] and the split-step backward Euler (SSBE) method [4]
Summary
For the past few years, stochastic age-dependent capital systems have become increasingly important mathematical tools to portray many financial phenomena in the real world. Zhang et al [4] constructed a split-step backward Euler (SSBE) method for stochastic age-dependent capital system with Markovian switching, and proved that the SSBE method converges with strong order of one half to the exact solution under the given conditions. As far as we know, few results on the convergence of SSθ method for stochastic age-dependent capital models with Poisson jumps and fBm have been reported. (Q1) Will the numerical solution converge to the exact solution when we apply the SSθ method to the stochastic age-dependent capital models with Poisson jumps and fBm (1)?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
