2:00 pm Monday, February 19, 2007
Internal Mathematical Finance Seminar: Maximizing the Growth Rate under Risk Constraints by Gordan Zitkovic (UT at Austin) in RLM 9.166
We investigate the ergodic problem of growth-rate maximization under a class of risk-constraints in the context of random-coefficient, incomplete, Ito-process models of financial markets. Including value-at-risk (VaR), tail-value-at-risk (TVaR), and limited expected loss, these constraints can be both wealth-dependent (relative) and wealth-independent (absolute). The optimal policy is shown to exist in an appropriate admissibility class, and can be obtained explicitly by uniform, state-dependent scaling down of the unconstrained (Merton) optimal portfolio. This implies that the risk-constrained wealth-growth optimizer locally behaves like a CRRA-investor, with the relative risk-aversion coefficient depending on the current values of the market coefficients. Submitted by
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