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Stochastic impulse control with regime-switching dynamics

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  • Korn, Ralf
  • Melnyk, Yaroslav
  • Seifried, Frank Thomas

Abstract

Optimal product management problems with multiple product generations in continuous time lead to the consideration of dynamic optimal control problems that feature both intervention costs and partially controlled regime shifts. We therefore investigate and solve such stochastic impulse control problems with regime-switching in a general setting. We analyze the associated coupled systems of quasi-variational inequalities in suitable Sobolev spaces, and we establish a direct approach to construct both the value function and optimal strategies. Our results in particular yield a numerical method for the computation of the optimal value function and the associated strategies.

Suggested Citation

  • Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:1024-1042
    DOI: 10.1016/j.ejor.2016.12.029
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    1. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    2. Chakravarty, Amiya K., 2001. "Overlapping design and build cycles in product development," European Journal of Operational Research, Elsevier, vol. 134(2), pages 392-424, October.
    3. Richard R. Lumley & Mihail Zervos, 2001. "A Model for Investments in the Natural Resource Industry with Switching Costs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 637-653, November.
    4. Seifert, Ralf W. & Tancrez, Jean-Sébastien & Biçer, Işık, 2016. "Dynamic product portfolio management with life cycle considerations," International Journal of Production Economics, Elsevier, vol. 171(P1), pages 71-83.
    5. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    6. Leslie Olin Morgan & Ruskin M. Morgan & William L. Moore, 2001. "Quality and Time-to-Market Trade-offs when There Are Multiple Product Generations," Manufacturing & Service Operations Management, INFORMS, vol. 3(2), pages 89-104, June.
    7. Carrillo, Janice E. & Franza, Richard M., 2006. "Investing in product development and production capabilities: The crucial linkage between time-to-market and ramp-up time," European Journal of Operational Research, Elsevier, vol. 171(2), pages 536-556, June.
    8. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    9. Min Dai & Zhou Yang & Qing Zhang & Qiji Jim Zhu, 2016. "Optimal Trend Following Trading Rules," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 626-642, May.
    10. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    11. Özer, Özalp & Uncu, Onur, 2015. "Integrating dynamic time-to-market, pricing, production and sales channel decisions," European Journal of Operational Research, Elsevier, vol. 242(2), pages 487-500.
    12. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
    13. Lim, Wei Shi & Tang, Christopher S., 2006. "Optimal product rollover strategies," European Journal of Operational Research, Elsevier, vol. 174(2), pages 905-922, October.
    14. Liao, Shuangqing & Seifert, Ralf W., 2015. "On the optimal frequency of multiple generation product introductions," European Journal of Operational Research, Elsevier, vol. 245(3), pages 805-814.
    15. Alain Bensoussan & SingRu Hoe & ZhongFeng Yan & George Yin, 2017. "Real Options With Competition And Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 224-250, January.
    16. Haolin Feng & Kumar Muthuraman, 2010. "A Computational Method for Stochastic Impulse Control Problems," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 830-850, November.
    17. Stefano Baccarin & Simona Sanfelici, 2006. "Optimal impulse control on an unbounded domain with nonlinear cost functions," Computational Management Science, Springer, vol. 3(1), pages 81-100, January.
    18. Nicolas P. B. Bollen, 1999. "Real Options and Product Life Cycles," Management Science, INFORMS, vol. 45(5), pages 670-684, May.
    19. Johnson, Timothy C. & Zervos, Mihail, 2010. "The explicit solution to a sequential switching problem with non-smooth data," LSE Research Online Documents on Economics 29003, London School of Economics and Political Science, LSE Library.
    20. Guo, Xin & Miao, Jianjun & Morellec, Erwan, 2005. "Irreversible investment with regime shifts," Journal of Economic Theory, Elsevier, vol. 122(1), pages 37-59, May.
    21. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    22. Reddy, Puduru V. & Wrzaczek, Stefan & Zaccour, Georges, 2016. "Quality effects in different advertising models - An impulse control approach," European Journal of Operational Research, Elsevier, vol. 255(3), pages 984-995.
    23. Melda Ormeci & J. G. Dai & John Vande Vate, 2008. "Impulse Control of Brownian Motion: The Constrained Average Cost Case," Operations Research, INFORMS, vol. 56(3), pages 618-629, June.
    24. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    25. Hu, Guiping & Bidanda, Bopaya, 2009. "Modeling sustainable product lifecycle decision support systems," International Journal of Production Economics, Elsevier, vol. 122(1), pages 366-375, November.
    26. R. Mark Krankel & Izak Duenyas & Roman Kapuscinski, 2006. "Timing Successive Product Introductions with Demand Diffusion and Stochastic Technology Improvement," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 119-135, June.
    27. Gilvan C. Souza & Barry L. Bayus & Harvey M. Wagner, 2004. "New-Product Strategy and Industry Clockspeed," Management Science, INFORMS, vol. 50(4), pages 537-549, April.
    28. Pan, Xiaojun & Li, Shoude, 2016. "Dynamic optimal control of process–product innovation with learning by doing," European Journal of Operational Research, Elsevier, vol. 248(1), pages 136-145.
    29. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    30. Chronopoulos, Michail & Lumbreras, Sara, 2017. "Optimal regime switching under risk aversion and uncertainty," European Journal of Operational Research, Elsevier, vol. 256(2), pages 543-555.
    31. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    32. Sergei Savin & Christian Terwiesch, 2005. "Optimal Product Launch Times in a Duopoly: Balancing Life-Cycle Revenues with Product Cost," Operations Research, INFORMS, vol. 53(1), pages 26-47, February.
    33. Salles, J. L. F. & do Val, J. B. R., 2001. "An impulse control problem of a production model with interruptions to follow stochastic demand," European Journal of Operational Research, Elsevier, vol. 132(1), pages 123-145, July.
    34. Ohnishi, Masamitsu & Tsujimura, Motoh, 2006. "An impulse control of a geometric Brownian motion with quadratic costs," European Journal of Operational Research, Elsevier, vol. 168(2), pages 311-321, January.
    35. Daniel Mitchell & Haolin Feng & Kumar Muthuraman, 2014. "Impulse Control of Interest Rates," Operations Research, INFORMS, vol. 62(3), pages 602-615, June.
    36. Erhan Bayraktar & Masahiko Egami, 2010. "On the One-Dimensional Optimal Switching Problem," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 140-159, February.
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