Grant: Discovery Grants Program - Individual

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. The second category of projects deals with the use of financial models where the switching of economic regimes is modulated by a hidden weak Markov chain in either discrete or continuous time. Weak Markov chains are capable of capturing the dynamics of financial processes with memory. Under this formulation, (i) the theory of stochastic filtering will be adopted to estimate model parameters; (ii) estimated parameters will then be used to price financial derivatives, calculate risk measures and design an optimal allocation of assets; and (iii) several important statistical inference questions will be addressed. Resolving the aforementioned issues would enable financial institutions to quantify and manage their risk profile accordingly and provide impetus to other researchers in the analysis of related problems in finance. This research work will be instrumental in the attainment of an efficient, well-functioning and stable financial market.