在金融数学和保险精算中，大多数的模型使用布朗运动或跳－扩散过程来刻画现实中的随机因素。本项目拟研究由马氏链驱动的金融市场，在该市场中随机因素由马氏链来刻画。与由布朗运动或跳扩散过程驱动的模型一样，由马氏链驱动的模型也可以刻画真实市场的许多特性。具体的，在这个市场中，我们将研究由马氏链驱动的金融市场中的最低保证死亡受益产品的定价、含有随机系数的时间不一致性的最优消费投资问题与均值－方差投资组合问题，以及含有记忆效应的金融市场中的投资组合管理问题。为了刻画上述三个问题的解，我们将研究由马氏链驱动的含有随机终端时间的倒向随机微分（差分）方程，一类新的倒向随机差分方程以及倒向随机Volterra积分方程。

Brownian motion and jump-diffusion processes are used to model the randomness of the real word in most of models in mathematical finance and actuarial science. In this project, we shall study the financial market driven by Markov chains, i.e. the randomness are modelled by Markov chains. Similar to the models driven by Brownian motion and jump-diffusion processes, the model driven by Markov chains can capture various features of the real world market. Specifically, in this market, we shall investigate the pricing of guaranteed minimum death benefits, time-inconsistent optimal consumption-investment problem and mean-variance portfolio selection with random coefficients and portfolio management in a financial market with memory. To characterise the solutions to the above three problems, we shall study backward stochastic differential (difference) equations with random terminal time, a new class of BSDEs and backward stochastic Volterra integral equations, which are all driven by Markov chains.