In this paper, we develop approximation methods for solving stochastic control problems. The systems under consideration involve regime switching, modulated by a continuous-time Markov chain. Using Markov chain approximation techniques, we construct discrete-time Markov chains having two components. In addition to convergence of the procedure, numerical experiments and remarks on controlled var...

Rough volatility models have recently been empirically shown to provide a good fit historical time series and implied smiles of SPX options. They are continuous-time stochastic models, whose process is driven by fractional Brownian motion with Hurst parameter less than half. Due the challenge that it neither semimartingale nor Markov process, there no unified method not only applies all rough b...

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying;...