Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
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DOI：
10.1214/09-aap619
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发表时间：
2008-09
影响因子：
1.8
通讯作者：
Samuel N. Cohen;R. Elliott
中科院分区：
文献类型：
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作者：
Samuel N. Cohen;R. Elliott
以往对倒向随机微分方程的研究，以及相关的非线性期望和动态风险度量理论，都是在连续时间扩散或跳跃扩散的框架下进行的。利用有限状态连续时间马氏链空间上的倒向随机微分方程的解，在[Dynamically consistent nonlinear evaluations and expectations（2005）Shandong Univ.]的基础上，建立了一个非线性期望理论.我们证明了这些期望的基本性质，并展示了它们在动态风险度量中的应用。特别是，我们证明了比较定理的标量和向量值的解决方案，BSDES，并讨论了套利和风险措施的标量情况下。
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.