Financial Engineering and
Financial data is noisy -- data is missing, data becomes outdated, models are wrong -- and yet one wants to compute “optimal” decisions using this noisy data. What is the impact of the noise in the data on the decisions? Can one correct for data errors within the optimization procedure? We have explored many applications of robust optimization in financial decision making.
A number of financial applications use simulations or samples to compute decisions. Implicitly, optimal is not achievable! Could one leverage this fact to design algorithms that compute approximate solutions very fast? Can one use the samples to compute bounds on the optimal solution? We explore various smoothing and information relaxation based techniques for problems ranging from approximating spectral risk measures to tax-aware equity portfolio selection
Since the 2008 crisis, “systemic risk” has become central to risk management and regulation -- and with come lots of different measures for systemic risk! We provide an axiomatic framework for understanding the assumptions underlying the proposed risk measures. We are now looking at how the endogenous price formation can lead to contagion and correlated defaults.