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A path integral approach to asset-liability management

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  • Decamps, Marc
  • De Schepper, Ann
  • Goovaerts, Marc

Abstract

Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-liability management. We work with a representation of cash flows by means of a two-dimensional delta-function perturbation, in the case of a Brownian model and a geometric Brownian model. We derive closed-form solutions for a finite horizon ALM policy. The results are numerically and graphically illustrated.

Suggested Citation

  • Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:404-416
    DOI: 10.1016/j.physa.2005.08.059
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    References listed on IDEAS

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    1. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    2. Kleinert, Hagen, 2002. "Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 217-242.
    3. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    4. G. Montagna & O. Nicrosini & N. Moreni, 2002. "A Path Integral Way to Option Pricing," Papers cond-mat/0202143, arXiv.org.
    5. Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    6. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    7. Montagna, Guido & Morelli, Marco & Nicrosini, Oreste & Amato, Paolo & Farina, Marco, 2003. "Pricing derivatives by path integral and neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 189-195.
    8. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    9. Michael I. Taksar, 2000. "Optimal risk and dividend distribution control models for an insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 1-42, February.
    10. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
    11. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
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    2. Benjamin Avanzi & Ping Chen & Lars Frederik Brandt Henriksen & Bernard Wong, 2022. "On the surplus management of funds with assets and liabilities in presence of solvency requirements," Papers 2203.05139, arXiv.org, revised Aug 2022.
    3. Xie, Shuxiang, 2009. "Continuous-time mean-variance portfolio selection with liability and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 148-155, August.
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    6. Hu, Fengxia & Wang, Rongming, 2017. "Optimal investment–consumption strategy with liability and regime switching model under Value-at-Risk constraint," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 103-118.
    7. Haven, Emmanuel, 2008. "Elementary Quantum Mechanical Principles and Social Science: Is There a Connection?," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 5(1), pages 41-58, March.
    8. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    9. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    10. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.

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