Past Mathematical Finance Seminar

18 June 2004
14:15
Abstract
In this talk we discuss the analytic approximation to the loss distribution of large conditionally independent heterogeneous portfolios. The loss distribution is approximated by the expectation of some normal distributions, which provides good overall approximation as well as tail approximation. The computation is simple and fast as only numerical integration is needed. The analytic approximation provides an excellent alternative to some well-known approximation methods. We illustrate these points with examples, including a bond portfolio with correlated default risk and interest rate risk. We give an analytic expression for the expected shortfall and show that VaR and CVaR can be easily computed by solving a linear programming problem where VaR is the optimal solution and CVaR is the optimal value.
  • Mathematical Finance Seminar
21 May 2004
14:15
Pauline Barrieu
Abstract
We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets.The modeling involves a minimization of the risk borne by issuer given the constraint imposed by a buyer who enters the transaction if and only if her risk level remains below a given threshold. Both agents have also the opportunity to invest all their residual wealth on financial markets but they do not have the same access to financial investments. The problem may be reduced to a unique inf-convolution problem involving some transformation of the initial risk measures.
  • Mathematical Finance Seminar

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