On the martingale and free-boundary approaches in sequential detection problems with exponential penalty for delay

We study the connection between the martingale and free-boundary approaches in sequential detection problems for the drift of a Brownian motion, under the assumption of exponential penalty for the delay. By means of the solution of a suitable free-boundary problem, we show that the reward process can be decomposed into the product between a gain function of the boundary point and a positive martingale inside the continuation region.     

随机市场系数的M-V最优投资组合选择:一个鞅方法

通过引进凹函数U(x)以及等价鞅测度p^-，应用鞅的性质得到了随机市场系数情形下的M—V模型的最优投资策略以及有效前沿．     

On representation and regularity of continuous parameter multivalued martingales

In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in convergence in the Hausdorff metric respectively.

     

鞅的矩型极大算子的若干不等式

给出了算子T=∑_(n=1)~∞T_n在H_B~p和BMO_(p,B)~-上有界的一些充分条件,其中T_n(n∈P)为具有Δ性质的算子.作为应用,借助于算子值鞅变换得到了关于鞅的矩型极大算子的强(p,p)型不等式和弱(1,1)型不等式,以及其在BMO_(p,B)~-上的有界性.这些结果与经典H~p鞅论中极大算子的性质相对应.     

带有重置条款的可转换债券定价

可转换债券是中国证券市场的热点之一.本文主要研究如何给带有重置条款的可转换债券进行定价.文中采用了等价鞅测度的思想将标的物从风险世界转换到风险中性世界中,然后在风险中性世界中应用鞅评价方法对带有重置条款的可转换债券进行定价.     

Minimal Martingale Measures for Discrete-time Incomplete Financial Markets

Abstract In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market.Then we concretely work out the minimal martingale messure for a specificdiscrete-time market model in which the assets'returns in different times are independent.     

Quadratic Hedging Methods for Defaultable Claims

We apply the local risk-minimization approach to defaultable claims and we compare it with intensity-based evaluation formulas and the mean-variance hedging. We solve analytically the problem of finding respectively the hedging strategy and the associated portfolio for the three methods in the case of a default put option with random recovery at maturity.     

非齐次树上m重非齐次马氏链的一类强偏差定理

研究给出了非齐次树上m重非齐次马氏链的一类强偏差定理.     

半参数回归模型小波估计的弱收敛速度

本文研究了误差为鞅差序列情形下的半参数回归模型.利用小波方法,在相当一般的条件下,得到了参数、非参数估计量的弱收敛速度.     

鞅分析在具有红利支付的n次幂型欧式期权定价中的应用

本文探讨了鞅分析在具有红利支付的n次幂型欧式期权定价中的应用,即用鞅分析的技巧与方法研究了在标的资产服从分数布朗运动的条件下具有红利支付的n次幂型欧式期权定价问题,并获得了其公式。丰富了已有期权定价结果,使期权定价公式更有利于实际的应用。