Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance

We propose dual decomposition and solution schemes for multistage CVaR-constrained problems. These schemes meet the need for handling multiple CVaR-constraints for different time frames and at different confidence levels. Hence they allow shaping distributions according to the decision maker's preference.With minor modifications, the proposed schemes can be used to decompose further types of risk constraints in dynamic portfolio management problems. We consider integrated chance constraints, second-order stochastic dominance constraints, and constraints involving a special value-of-information risk measure. We also suggest application to further financial problems. We propose a dynamic risk-constrained optimization model for option pricing. Moreover we propose special mid-term constraints for use in asset-liability management.

[1]  A. Charnes,et al.  Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil , 1958 .

[2]  András Prékopa,et al.  Contributions to the theory of stochastic programming , 1973, Math. Program..

[3]  W. K. Haneveld.  Duality in Stochastic Linear and Dynamic Programming , 1986 .

[4]  Yurii Nesterov,et al.  New variants of bundle methods , 1995, Math. Program..

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

[6]  Helmut Mausser,et al.  Credit risk optimization with Conditional Value-at-Risk criterion , 2001, Math. Program..

[7]  P. Krokhmal,et al.  Portfolio optimization with conditional value-at-risk objective and constraints , 2001 .

[8]  S. Zenios,et al.  The Tail that Wags the Dog: Integrating Credit Risk in Asset Portfolios , 2001 .

[9]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[10]  Maarten H. van der Vlerk,et al.  ALM model for pension funds: numerical results for a prototype model , 2002 .

[11]  Wlodzimierz Ogryczak,et al.  Dual Stochastic Dominance and Related Mean-Risk Models , 2002, SIAM J. Optim..

[12]  S. Uryasev,et al.  Pricing European Options by Numerical Replication: Quadratic Programming with Constraints , 2004 .

[13]  A. Ruszczynski,et al.  Portfolio optimization with stochastic dominance constraints , 2006 .

[14]  Georg Ch. Pflug,et al.  A value-of-information approach to measuring risk in multi-period economic activity , 2006 .

[15]  Shabbir Ahmed,et al.  Convexity and decomposition of mean-risk stochastic programs , 2006, Math. Program..

[16]  Alexandra Künzi-Bay,et al.  Computational aspects of minimizing conditional value-at-risk , 2006, Comput. Manag. Sci..

[17]  Hercules Vladimirou,et al.  A Stochastic Programming Framework for International PortfolioManagement , 2006 .

[18]  G. Mitra,et al.  Mean-risk models using two risk measures: a multi-objective approach , 2007 .

[19]  Csaba I. Fábián,et al.  Solving two-stage stochastic programming problems with level decomposition , 2007, Comput. Manag. Sci..

[20]  Csaba I. Fábián.  Handling CVaR objectives and constraints in two-stage stochastic models , 2008, Eur. J. Oper. Res..

[21]  Hercules Vladimirou,et al.  A dynamic stochastic programming model for international portfolio management , 2008, Eur. J. Oper. Res..

[22]  Maarten H. van der Vlerk,et al.  An ALM model for pension funds using integrated chance constraints , 2010, Ann. Oper. Res..