IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.05926.html
   My bibliography  Save this paper

SCOP: Schrodinger Control Optimal Planning for Goal-Based Wealth Management

Author

Listed:
  • Igor Halperin

Abstract

We consider the problem of optimization of contributions of a financial planner such as a working individual towards a financial goal such as retirement. The objective of the planner is to find an optimal and feasible schedule of periodic installments to an investment portfolio set up towards the goal. Because portfolio returns are random, the practical version of the problem amounts to finding an optimal contribution scheme such that the goal is satisfied at a given confidence level. This paper suggests a semi-analytical approach to a continuous-time version of this problem based on a controlled backward Kolmogorov equation (BKE) which describes the tail probability of the terminal wealth given a contribution policy. The controlled BKE is solved semi-analytically by reducing it to a controlled Schrodinger equation and solving the latter using an algebraic method. Numerically, our approach amounts to finding semi-analytical solutions simultaneously for all values of control parameters on a small grid, and then using the standard two-dimensional spline interpolation to simultaneously represent all satisficing solutions of the original plan optimization problem. Rather than being a point in the space of control variables, satisficing solutions form continuous contour lines (efficient frontiers) in this space.

Suggested Citation

  • Igor Halperin, 2023. "SCOP: Schrodinger Control Optimal Planning for Goal-Based Wealth Management," Papers 2309.05926, arXiv.org.
    • Handle: RePEc:arx:papers:2309.05926
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.05926
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    2. Halperin, Igor, 2022. "Non-equilibrium skewness, market crises, and option pricing: Non-linear Langevin model of markets with supersymmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Torgler, Benno & Schneider, Friedrich & Schaltegger, Christoph A., 2007. "With or Against the People? The Impact of a Bottom-Up Approach on Tax Morale and the Shadow Economy," Berkeley Olin Program in Law & Economics, Working Paper Series qt6331x6vz, Berkeley Olin Program in Law & Economics.
    2. Daniel Fonseca Costa & Francisval Carvalho & Bruno César Moreira & José Willer Prado, 2017. "Bibliometric analysis on the association between behavioral finance and decision making with cognitive biases such as overconfidence, anchoring effect and confirmation bias," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1775-1799, June.
    3. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    4. Jae Wook Yoo & Richard Reed & Shung Jae Shin & David J. Lemak, 2009. "Strategic Choice and Performance in Late Movers: Influence of the Top Management Team's External Ties," Journal of Management Studies, Wiley Blackwell, vol. 46(2), pages 308-335, March.
    5. Giovanni Calice & Levent Kutlu & Ming Zeng, 2021. "Understanding US firm efficiency and its asset pricing implications," Empirical Economics, Springer, vol. 60(2), pages 803-827, February.
    6. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    7. José Castro Caldas & Helder Coelho, 1999. "The Origin of Institutions: Socio-Economic Processes, Choice, Norms and Conventions," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 2(2), pages 1-1.
    8. Nagler Matthew G., 2007. "Understanding the Internet's Relevance to Media Ownership Policy: A Model of Too Many Choices," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 7(1), pages 1-28, June.
    9. Ranganathan, Kavitha & Lejarraga, Tomás, 2021. "Elicitation of risk preferences through satisficing," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
    10. Westerhoff Frank H., 2008. "The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 228(2-3), pages 195-227, April.
    11. Andrew Caplin & Mark Dean & Daniel Martin, 2011. "Search and Satisficing," American Economic Review, American Economic Association, vol. 101(7), pages 2899-2922, December.
    12. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    13. Lawrence Bunnell & Kweku-Muata Osei-Bryson & Victoria Y. Yoon, 0. "RecSys Issues Ontology: A Knowledge Classification of Issues for Recommender Systems Researchers," Information Systems Frontiers, Springer, vol. 0, pages 1-42.
    14. da Silveira, Jaylson Jair & Lima, Gilberto Tadeu, 2021. "Wage inequality as a source of endogenous macroeconomic fluctuations," Structural Change and Economic Dynamics, Elsevier, vol. 56(C), pages 35-52.
    15. Nathan N. Cheek & Jacob Goebel, 2020. "What does it mean to maximize? “Decision difficulty,†indecisiveness, and the jingle-jangle fallacies in the measurement of maximizing," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 15(1), pages 7-24, January.
    16. Marianne Bertrand & Dean S. Karlan & Sendhil Mullainathan & Eldar Shafir & Jonathan Zinman, 2005. "What's Psychology Worth? A Field Experiment in the Consumer Credit Market," Working Papers 918, Economic Growth Center, Yale University.
    17. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    18. Manolis, Chris & Nygaard, Arne & Stillerud, Bård, 1997. "Uncertainty and vertical control: An international investigation," International Business Review, Elsevier, vol. 6(5), pages 501-518, October.
    19. Umar, Tarik, 2022. "Complexity aversion when SeekingAlpha," Journal of Accounting and Economics, Elsevier, vol. 73(2).
    20. Izat B. Baybusinov & Enrico Maria Fenoaltea & Yi-Cheng Zhang, 2022. "Negotiation problem," Papers 2201.12619, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2309.05926. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.