Risk Measure

1) ON MEASURING RISK WITH SCARCE OBSERVATIONS

We consider the problem of measuring the risk of a portfolio with scarce observations by linking it to several risk factors. A typical example is measuring the risk of a hedge fund. It is assumed that from the available data one can estimate the joint law of all the factors as well as all the 2-dimensional joint laws of the portfolio's return and increments of each factor. The problem is to recover the conditional mean of the portfolio's return given the values for all factors. We present an analytic computationally feasible solution of this problem for the case when the joint law of factors is a Gaussian copula.

2) Measuring Extreme Risks: Nonlinear statistics and Factor models

Measuring extreme risks is a different problem from estimating fat tails. Extreme events can, occasionally, have a probability of occurrence that make them a possible distribution center. In this lecture, we shall present how to use long term factor data and nonlinear statistical estimates to evaluate the possible impact of market blow-ups on assets, funds and porfolios.

3) Portfolio construction under extreme risk control

 We shall present an adaptation of Markowitz portfolio optimization principle to extreme risk measures. The now widely used "risk budgeting" technique can also efficiently be adapted to such risks with very effective effects in case of crises.

报告时间：2009年4月30日（星期四）上午9：00-12：00；下午14：00-16：00