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Time-Inconsistent Portfolio Investment Problems

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Stochastic Analysis and Applications 2014

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 100))

Abstract

The explicit results for the classical Merton optimal investment/consumption problem rely on the use of constant risk aversion parameters and exponential discounting. However, many studies have suggested that individual investors can have different risk aversions over time, and they discount future rewards less rapidly than exponentially. While state-dependent risk aversions and non-exponential type (e.g. hyperbolic) discountings align more with the real life behavior and household consumption data, they have tractability issues and make the problem time-inconsistent. We analyze the cases where these problems can be closely approximated by time-consistent ones. By asymptotic approximations, we are able to characterize the equilibrium strategies explicitly in terms of the corrections to solutions for the base problems with constant risk aversion and exponential discounting. We also explore the effects of hyperbolic discounting under proportional transaction costs.

Partially supported by NSF grant DMS-1211906.

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Notes

  1. 1.

    These models can be seen as a particular example of the studies on state-dependent utility/preference by Karni [20]. In this case the dependency has an explicit functional form as \(\gamma (\cdot )\).

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Authors and Affiliations

  1. Department of Operations Research and Financial Engineering, Princeton University, Princeton, 08544, NJ, USA

    Yidong Dong & Ronnie Sircar

Authors
  1. Yidong Dong
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  2. Ronnie Sircar
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Correspondence to Yidong Dong .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College, London, United Kingdom

    Dan Crisan

  2. Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Ben Hambly

  3. Department of Mathematics and IROM, University of Texas McCombs School of Business, Austin, Texas, USA

    Thaleia Zariphopoulou

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Dong, Y., Sircar, R. (2014). Time-Inconsistent Portfolio Investment Problems. In: Crisan, D., Hambly, B., Zariphopoulou, T. (eds) Stochastic Analysis and Applications 2014. Springer Proceedings in Mathematics & Statistics, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-11292-3_9

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