Hidden markov models in quantitative finance

我的研究项目包括调查市场变量动态建模问题的相关项目，这是金融估值、风险管理和资产配置中的一个基本问题。这些项目可以分为两大类。第一类项目考虑使用与假定遵循隐马尔可夫模型的经济体制转变相协调的金融模型。在这一框架下，希望(I)通过求解偏微分方程组来获得金融合同公平价格的数值近似，(Ii)死亡率和利率都具有不一定相互独立的随机演变的价值保险和与养老金相关的产品，以及(Iii)使用Esscher变换或构造其他风险中性度量来在马尔可夫市场的不完备环境下进行估值。

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.