Maximizing portfolio growth rate under risk constraints

• Main Author: Pirvu, Traian A
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2005
• Subjects: Brownian motion; Copyright; Economic theory; Expected utility; Finance; Inequality; Interest rates; Investment policy; Investments; Lagrange multiplier; Mathematics; Random variables; Rates of return; Regulation of financial institutions; Risk management; Securities markets; Studies; Volatility
• ISBN: 0542015595; 9780542015595

This thesis studies the problem of optimal investment subject to risk constraints: Value-at-Risk, Tail Valve-at-Risk and Limited Expected Loss. We get closed-form solutions for this problem, and find that the optimal policy is a projection of the optimal portfolio of an unconstrained log agent (the Merton proportion) onto the constraint set, with respect to the inner product induced by the variance-covariance volatilities matrix of the risky assets. In the more complicated situation of constraint sets depending on the current wealth level, we maximize the growth rate of portfolio subject to these risk constraints. We extend the analysis to a market with random coefficients, which is not necessarily complete. We also perform a robust control analysis. We find that a trader subject to Value-at-Risk and Tail Value-at-Risk is allowed to incur some risk. A trader faced with the Limited Expected Loss constraint behaves more conservatively and does not exhibit the above behavior.