Risk minimizing portfolio optimization and hedging with Conditional Value-at-Risk.

摘要

This thesis looks at the problem of finding the optimal investment strategy of a self-financing portfolio in a dynamic complete market setting so that the risk measured by Conditional Value-at-Risk (CVaR) is minimized under the condition that the expected return is bounded from below.;We start out with a CVaR minimization problem without expected return requirement. We find the exact optimal conditions and apply them to two classic complete market models: the Binomial model and the Black-Scholes model. In these cases, the procedures of finding the optimal strategies are given with exact formulas, and the resulting minimal CVaR values can be calculated.;We then add a minimal expected return constraint, and look for an optimal solution in a continuous-time setting. The optimal solution most likely does not exist if there is no upper bound on returns over time, but the infimum of CVaR can still be computed. However, when such a uniform upper bound is prescribed, we find the optimal conditions together with the optimal investment strategy and the resulting minimal CVaR.