
 Large Portfolio Losses by Amir Dembo of Stanford University, January 2004 Abstract: This paper provide a largedeviations 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 largedeviations estimate of the likelihood that there will exist a subperiod 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 an initial time interval whose length is a property of the portfolio and the critical loss level. JEL Classification: G21, G22, G33. AMS Classification: 60F10, 91B28. Keywords: Large deviations, insurance, risk measure, portfolio loss. Published in: Finance and Stochastics, Vol. 8, No. 1, (January 2004), pp. 316. Books Referenced in this paper: (what is this?) 