Large Portfolio Losses

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.