2019/08/29 by Giang T. Nguyen, Oscar Peralta, Nguyen, Giang T. +1 · 1 citation
Social Sciences · Economics, Econometrics and Finance · #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.1908.11075
In Latouche and Nguyen (2015), the authors constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). Here, we construct a different sequence of stochastic fluid processes and show that it converges strongly to an MMBM. To the best of our knowledge, this is the first result on strong convergence to a Markov-modulated Brownian motion. We also prove that the rate of this almost sure convergence is o(n-1/2 log n). When reduced to the special case of standard Brownian motion, our convergence rate is an improvement over that obtained by a different approximation in \citegorostiza1980rate, which is o(n-1/2(log n)5/2).