Solving ALM problems via sequential stochastic programming

In this paper, an approximation of dynamic programming using sequential stochastic programming is introduced to solve long-term dynamic financial planning problems. We prove that by approximating the true asset return dynamics by a set of scenarios and re-solving the problem at every time-step, we can solve in principle the dynamic programming problem with an arbitrarily small error. The dynamic programming algorithm is effected on the approximate sample return dynamics by means of stochastic programming. This method is applied to the problem of a fund that guarantees a minimal return on investments. This minimal return guarantee is the liability of the fund. The dynamic portfolio management problem consists of maximizing the multi-period return while limiting the shortfall with regard to the guaranteed return. The problem is tested in an 8 year out-of-sample backtest from the perspective of a Swiss fund that invests domestically and in the EU markets and faces transaction costs.

[1]  Michal Kaut,et al.  A Heuristic for Moment-Matching Scenario Generation , 2003, Comput. Optim. Appl..

[2]  M. Dempster.  Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming , 2006 .

[3]  M. Dempster,et al.  Designing minimum guaranteed return funds , 2007 .

[4]  T ZiembaWilliam,et al.  The Stochastic Programming Approach to Asset, Liability, and Wealth Management , 2006 .

[5]  S. Weiland,et al.  Optimal control of linear, stochastic systems with state and input constraints , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  J. Mulvey.  Generating Scenarios for the Towers Perrin Investment System , 1996 .

[7]  Dimitri P. Bertsekas,et al.  Stochastic optimal control : the discrete time case , 2007 .

[8]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[10]  William T. Ziemba,et al.  Formulation of the Russell-Yasuda Kasai Financial Planning Model , 1998, Oper. Res..

[11]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[12]  Bala Shetty,et al.  Financial planning via multi-stage stochastic optimization , 2004, Comput. Oper. Res..

[13]  Frank Riedel,et al.  Dynamic Coherent Risk Measures , 2003 .

[14]  Matti Koivu,et al.  Variance reduction in sample approximations of stochastic programs , 2005, Math. Program..

[15]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[16]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[17]  Florian Herzog,et al.  Dynamic asset and liability management for swiss pension funds , 2008 .

[18]  Teemu Pennanen,et al.  Epi-convergent discretizations of stochastic programs via integration quadratures , 2005, Numerische Mathematik.

[19]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[20]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[21]  Werner Römisch,et al.  Scenario tree reduction for multistage stochastic programs , 2009, Comput. Manag. Sci..

[22]  M. Dempster,et al.  Managing Guarantees , 2006 .

[23]  John R. Birge,et al.  A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs , 1996, Math. Program..

[24]  Michael A. H. Dempster,et al.  EVPI‐based importance sampling solution proceduresfor multistage stochastic linear programmeson parallel MIMD architectures , 1999, Ann. Oper. Res..

[25]  Gabriel Dondi.  Models and dynamic optimisation for the asset and liability management of pension funds , 2005 .

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

[27]  Galin L. Jones.  Book Review of Givens, G. H. and Hoeting, J. A. (2005), Computational Statistics, Wiley , 2006 .

[28]  Bloor Street,et al.  An Asset and Liability Management System for Towers Perrin-Tillinghast , 2000 .

[29]  John M. Mulvey,et al.  An Asset and Liability Management System for Towers Perrin-Tillinghast , 2000, Interfaces.

[30]  William T. Ziemba,et al.  Handbook of Asset and Liability Management - Set , 2007 .

[31]  Paul Bratley,et al.  Algorithm 659: Implementing Sobol's quasirandom sequence generator , 1988, TOMS.

[32]  William T. Ziemba,et al.  The Innovest Austrian Pension Fund Financial Planning Model InnoALM , 2008, Oper. Res..

[33]  Teemu Pennanen,et al.  Epi-Convergent Discretizations of Multistage Stochastic Programs , 2005, Math. Oper. Res..

[34]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

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

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

[37]  W. Römisch.  Stability of Stochastic Programming Problems , 2003 .