Portfolio optimization with irreversible long-term investments in renewable energy under policy risk: A mixed-integer multistage stochastic model and a moving-horizon approach

Abstract Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer multistage stochastic model that includes investment opportunities in irreversible and long-term infrastructure projects in the context of renewable energies, which are also subject to policy risk. On realistic time scales for investment problems of this type, the resulting instances are by far too large to be solved with today’s most evolved optimization software. Thus, we present a tailored moving-horizon approach together with suitable approximations and simplifications of the model. We evaluate these approximations and simplifications in a computational sensitivity analysis and derive a final model that can be tackled on a realistic instance by our moving-horizon approach.

[1]  Ignacio E. Grossmann,et al.  Stochastic programming models for optimal shale well development and refracturing planning under uncertainty , 2017 .

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

[3]  G. Hunanyan,et al.  Portfolio Selection , 2019, Finanzwirtschaft, Banken und Bankmanagement I Finance, Banks and Bank Management.

[4]  V. Grimm,et al.  The role of expectations for market design – on structural regulatory uncertainty in electricity markets , 2019 .

[5]  Maria Grazia Speranza,et al.  Twenty years of linear programming based portfolio optimization , 2014, Eur. J. Oper. Res..

[6]  J Figueira,et al.  Stochastic Programming , 1998, J. Oper. Res. Soc..

[7]  Z Degraeve,et al.  Project Valuation in Mixed Asset Portfolio Selection , 2005 .

[8]  Thomas D. Sandry,et al.  Probabilistic and Randomized Methods for Design Under Uncertainty , 2007, Technometrics.

[9]  Luis M. Abadie,et al.  Valuation of Wind Energy Projects: A Real Options Approach , 2014 .

[10]  A. Jung,et al.  Investment strategies under transaction costs: the finite horizon case , 1994 .

[11]  N. Yoshida.  Estimation for diffusion processes from discrete observation , 1992 .

[12]  Stephen J. Wright,et al.  Nonlinear Predictive Control and Moving Horizon Estimation — An Introductory Overview , 1999 .

[13]  R. Schultz,et al.  Multistage Stochastic Integer Programs: An Introduction , 2001 .

[14]  Marvin D. Troutt,et al.  Objective comparisons of the optimal portfolios corresponding to different utility functions , 2009, Eur. J. Oper. Res..

[15]  Pedro Santa-Clara,et al.  Dynamic Portfolio Selection by Augmenting the Asset Space , 2006 .

[16]  G. Martin,et al.  Nonlinear model predictive control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Nadine Gatzert,et al.  Insurers’ Investment in Infrastructure: Overview and Treatment under Solvency II , 2014 .

[18]  Sebastian Engell,et al.  Medium-term planning of a multiproduct batch plant under evolving multi-period multi-uncertainty by means of a moving horizon strategy , 2010, Comput. Chem. Eng..

[19]  Claudia A. Sagastizábal,et al.  The value of rolling-horizon policies for risk-averse hydro-thermal planning , 2012, Eur. J. Oper. Res..

[20]  Shabbir Ahmed,et al.  Stochastic dual dynamic integer programming , 2019, Math. Program..

[21]  Stephen P. Boyd,et al.  Portfolio optimization with linear and fixed transaction costs , 2007, Ann. Oper. Res..

[22]  Chang-Chun Lin,et al.  Genetic algorithms for portfolio selection problems with minimum transaction lots , 2008, Eur. J. Oper. Res..

[23]  Taras Bodnar,et al.  A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function , 2012, Ann. Oper. Res..

[24]  Michal Kaut,et al.  Multi-horizon stochastic programming , 2014, Comput. Manag. Sci..

[25]  James E. Smith,et al.  Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds , 2011, Manag. Sci..

[26]  Harry M. Markowitz,et al.  Mean-variance approximations to expected utility , 2014, Eur. J. Oper. Res..

[27]  Nadine Gatzert,et al.  Risks and risk management of renewable energy projects: The case of onshore and offshore wind parks , 2016 .

[28]  F. Longstaff.  Optimal Portfolio Choice and the Valuation of Illiquid Securities , 2001 .

[29]  Michael Obersteiner,et al.  Renewable energy investment: Policy and market impacts , 2012 .

[30]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

[31]  Nadine Gatzert,et al.  Evaluating Investments in Renewable Energy Under Policy Risks , 2016 .

[32]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[33]  Werner Römisch,et al.  Airline network revenue management by multistage stochastic programming , 2008, Comput. Manag. Sci..

[34]  Trine Krogh Boomsma,et al.  Renewable energy investments under different support schemes: A real options approach , 2012, Eur. J. Oper. Res..

[35]  Masao Fukushima,et al.  A mixed R&D projects and securities portfolio selection model , 2008, European Journal of Operational Research.

[36]  Nadine Gatzert,et al.  Risk- and Value-Based Management for Non-Life Insurers under Solvency Constraints , 2017, Eur. J. Oper. Res..

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

[38]  B. Mcguinness,et al.  Twenty years on. , 1976, British medical journal.

[39]  Antonio Espuña Camarasa,et al.  A rolling horizon stochastic programming framework for the energy supply and demand management in microgrids , 2015 .

[40]  George B. Dantzig,et al.  Multi-stage stochastic linear programs for portfolio optimization , 1993, Ann. Oper. Res..

[41]  Maria Grazia Speranza,et al.  Heuristic algorithms for the portfolio selection problem with minimum transaction lots , 1999, Eur. J. Oper. Res..

[42]  R. Schultz,et al.  Multistage stochastic integer programs , 2001 .

[43]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[44]  A. Nemirovski,et al.  Scenario Approximations of Chance Constraints , 2006 .

[45]  Manuel Monjas-Barroso,et al.  Valuation of projects for power generation with renewable energy: A comparative study based on real regulatory options , 2013 .

[46]  Pedro Santa-Clara,et al.  Anderson Graduate School of Management – Finance Uc Los Angeles Title: Dynamic Portfolio Selection by Augmenting the Asset Space Dynamic Portfolio Selection by Augmenting the Asset Space * , 2022 .