Non-Lipschitz条件下BSDE解的一个命题的证明

假设生成元-g函数满足更一般的non-Lipschitz条件,通过Hlder不等式,证明了关于BSDE解的一个命题.命题结论在non-Lipschitz条件下对证明BSDE逆比较定理及生成元的唯一性起到了至关重要的作用.     

Knight不确定性与一般风险资产的动态最小定价

文章研究了具有Knight不确定性的金融市场,利用倒向随机微分方程(BSDE)的重要理论以及时间-风险折现方法,探讨了一般风险资产的动态定价公式,求出了一般风险资产在Knight不确定性控制集合上的动态最小定价.最后通过研究某种风险资产的动态最小定价公式,借助于数值分析,揭示了Knight不确定性对风险资产定价的重要影响.     

不确定环境下再装股票期权的稳健定价模型

研究具有Knight不确定性的金融市场,假定标的资产(股票)价格过程服从几何布朗运动,建立了再装股票期权在一个概率测度集合上的最大、最小定价模型。并借助于倒向随机微分方程(BSDE)以及偏微分方程(PDE)的重要理论完成了对模型的转化。最后利用随机过程的有关知识求出了该模型的显示表达式,并通过具体的数值分析揭示了Knight不确定性对再装股票期权定价的重要影响。     

An optimal investment and risk control policy for a bank under exponential utility

Motivated by the Basel Capital Accord Requirement (CAR), we analyze a risk control portfolio selection problem under exponential utility when a banker faces both Brownian and jump risks. The banker's risk process and the dynamics of the risky asset process are modeled as jump-diffusion processes. Assuming that the constraint set of all trading strategies is in a closed set, we study the terminal utility optimization problem via the backward stochastic differential equation (BSDE) under risk regulation paradigm. We construct the BSDE by means of the martingale optimality principle, giving conditions for the corresponding generator to be well defined in order to derive the bounds on the candidate optimal strategy. We then construct an internal model for the bank under Basel III CAR, which is formulated from the total risk-weighted assets (TRWA's) and bank capital. The results obtained from this model can be adopted within the banking sector when setting up asset investment strategies and advanced risk management models, as advocated by the Basel III Accord.