We are concerned with losses from defaults in a small or large portfolio of defaultable obligors. A static structural model is employed in which for each obligor a latent variable is introduced to govern its default and loss rate. For a small portfolio, we use multivariate regular variation to describe the microstructure of the latent variables and derive a limit distribution of the portfolio loss as the default probability becomes small. For a large portfolio, however, modeling the microstructure of the latent variables becomes less appropriate; hence, we instead use a mixture structure that incorporates idiosyncratic risk, systematic risk, and common shock. For this case, the portfolio effect, namely the decrease in overall risk due to the portfolio size increase, is taken into account by assuming that the default threshold varies with the portfolio size. We derive sharp asymptotics for the tail probability of the portfolio loss as the portfolio size becomes large.

This talk is based on the following joint papers: Tang and Yuan (2013, North American Actuarial Journal), Shi, Tang and Yuan (2017, Insurance: Mathematics and Economics), and Tang and Yang (2017, Working Paper ).


Qihe Tang

Research Area



University of New South Wales


Fri, 04/05/2018 - 4:00pm


RC-4082, The Red Centre, UNSW