Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.