Large Portfolio Losses
Amir Dembo, Jean-Deominique Deuschel, Darrell Duffie
NBER Working Paper No. 9177
This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating exposure limits, and in allocating risk capital across different lines of business. Assuming that, for a given total loss, the distress caused by the loss is larger if the loss occurs within a smaller time period, we provide a large-deviations estimate of the likelihood that there will exist a sub-period of the future planning period during which a total loss of the critical severity occurs. Under conditions, this calculation is reduced to the calculation of the likelihood of the same sized loss over a fixed initial time interval whose length is a property of the portfolio and the critical loss level.
Published: Dembo, Amir, Jean-Dominique Deuschel and Darrell Duffie. "Large Portfolio Losses," Finance and Stochastics, 2004, v8(1), 3-16.