Dynamic Average Value-at-Risk Allocation on Worst Scenarios in Asset Management

A dynamic portfolio optimization model with average value-at-risks is discussed for drastic declines of asset prices. Analytical solutions for the optimization at each time are obtained by mathematical programming. By dynamic programming, an optimality equation for optimal average value-at-risks over time is derived. The optimal portfolios and the corresponding average value-at-risks are given as solutions of the optimality equation. A numerical example is given to understand the solutions and the results.

[1]  Yuji Yoshida,et al.  An Ordered Weighted Average with a Truncation Weight on Intervals , 2012, MDAI.

[2]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[3]  John Cotter,et al.  Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements , 2006, 1103.5653.

[4]  Y. Yoshida.  An Optimal Process for Average Value-at-Risk Portfolios in Financial Management , 2017 .

[5]  S. Pliska.  Introduction to Mathematical Finance: Discrete Time Models , 1997 .

[6]  Amir Ahmadi-Javid,et al.  Entropic Value-at-Risk: A New Coherent Risk Measure , 2012, J. Optim. Theory Appl..

[7]  D. Tasche,et al.  Expected shortfall and beyond , 2002, cond-mat/0203558.

[8]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[9]  W. Sharpe,et al.  Mean-Variance Analysis in Portfolio Choice and Capital Markets , 1987 .

[10]  Laurent El Ghaoui,et al.  Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach , 2003, Oper. Res..

[11]  A. Meucci.  Risk and asset allocation , 2005 .

[12]  A. Whitehead.  An Introduction to Mathematics , 1949, Nature.

[13]  Yuji Yoshida.  A Dynamic Value-at-Risk Portfolio Model , 2011, MDAI.

[14]  Marc C. Steinbach,et al.  Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis , 2001, SIAM Rev..

[15]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[16]  Yuji Yoshida.  A Dynamic Risk Allocation of Value-at-Risks with Portfolios , 2012, J. Adv. Comput. Intell. Intell. Informatics.