Hidden markov models in quantitative finance

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My research program comprises of related projects investigating issues on the dynamic modelling of market variables, which is a fundamental concern in financial valuation, risk management and asset allocation. These projects can be grouped into two general categories. The first category of projects considers the use of financial models that incoporate the shift of economic regimes assumed to follow a hidden Markov model. Under this framework, it is desired to (i) obtain numerical approximation for the fair price of financial contracts by solving a system of partial or ordinary differential equations, (ii) value insurance and pension-related products where both mortality and interest rates have stochastic evolution not necessarily independent of each other and (iii) employ Esscher transform or construct other risk-neutral measures to perform valuation in the incomplete setting of a Markov market.