特殊形式的倒向随机微分方程在金融市场中的应用

首先,针对一类线性倒向随机微分方程,给出了g-鞅同鞅之间相互联系所满足的充分条件.通过该条件得到了经典的Black-Scholes模型下未定权益的公平价格过程以及最优增长投资策略的价格过程.其次,引入了带惩罚的非线性倒向随机微分方程,并通过惩罚比率的不同取值来讨论相关的经济学意义.

THE APPLICATION OF SPECIAL BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN FINANCE

Firstly,aiming at a class of linear backward stochastic differential equation,the sufficient condition is given,which should be satisfied if some connection exists between g-martingale and martingale.With the condition,the fair price process of a contingent claim in classical Black-Scholes model and the value process of growth optimal portfolio are obtained.Secondly,a class of nonlinear backward stochastic differential equation with penalty is presented,and the correlated economic meanings are discussed for...