论文标题
瞬态Cramér-lundberg模型，其应用于信用风险
A transient Cramér-Lundberg model with applications to credit risk
论文作者
论文摘要
本文考虑了经典的Cramér-Lundberg模型的一种变体，该变体在信用环境中特别适合，其区别功能与有限数量的债务人相对应。重点是计算毁灭概率，即初始储备会因从债务人那里获得的利息而增加的概率，并因违约而减少的损失降低，下降到零以下。除了对这种破坏概率的精确分析（在转换方面）外，还进行了渐近分析，包括基于有效的基于重要性采样的仿真方法。 The base model is extended in multiple dimensions: (i) we consider a model in which there may, in addition, be losses that do not correspond to defaults, (ii) then we analyze a model in which the individual obligors are coupled through a regime-switching mechanism, (iii) then we extend the model such that between the losses the reserve process behaves as a Brownian motion rather than a deterministic drift, and (iv) we finally consider a set-up with multiple groups统计上相同的义务。
This paper considers a variant of the classical Cramér-Lundberg model that is particularly appropriate in the credit context, with the distinguishing feature that it corresponds to a finite number of obligors. The focus is on computing the ruin probability, i.e., the probability that the initial reserve, increased by the interest received from the obligors and decreased by the losses due to defaults, drops below zero. Besides an exact analysis (in terms of transforms) of this ruin probability, also an asymptotic analysis is performed, including an efficient importance-sampling based simulation approach. The base model is extended in multiple dimensions: (i) we consider a model in which there may, in addition, be losses that do not correspond to defaults, (ii) then we analyze a model in which the individual obligors are coupled through a regime-switching mechanism, (iii) then we extend the model such that between the losses the reserve process behaves as a Brownian motion rather than a deterministic drift, and (iv) we finally consider a set-up with multiple groups of statistically identical obligors.
