Lead PI: Prof. Paolo Guasoni

Empirical evidence shows that asset prices are periodically subject to large movements, which are hard to reconcile with models based on diffusions. The recent volatility in the financial market provides a case in point. Alternative models which account for jumps are mainly based on Levy processes. While these models lead to a better empirical fit and to more accurate pricing formulas, their implications for asset allocation are not satisfactory, since optimal portfolios are independent of the investment horizon. This feature is inconsistent with conventional wisdom in asset management, which prescribes different asset allocations for investors with long and short horizons.

Korn and Wilmott (2002) introduce the notion of the worst-case scenario portfolio problem, where optimal portfolios explicitly depend on the investment horizon. Korn and Menkens (2005) develop the related concept of crash hedging strategies, which make an investor indifferent, in terms of expected utility, to the occurrence of a crash.

Further development of this theory and the focus of this WP entails consideration of:

(i) Accounting for consumption;

(ii) extending the analysis to exponential utility functions, commonly employed in actuarial applications;

(iii) analyzing the behaviour of crash hedging in the limit of small jumps.