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Maximizing the Growth Rate under Risk Constraints


  • Traian A. Pirvu
  • Gordan Zitkovic


We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, It\^{o}-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), 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.

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  • Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480,
  • Handle: RePEc:arx:papers:0706.0480

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