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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Mathematical Finance
Volume 10 - 2024 | doi: 10.3389/fams.2024.1415385
This article is part of the Research Topic Financial Modeling with Frictions View all articles

Stochastic Optimal Control Problem of Consumption and Pension Insurance with Uncertain Lifetime and Its Application to Real-Life Data

Provisionally accepted
Gereltuya Terbish Gereltuya Terbish 1*Batsukh Tserendorj Batsukh Tserendorj 2Nyamsuren Dorj Nyamsuren Dorj 1Tserenbat Oirov Tserenbat Oirov 1
  • 1 Mongolian University of Science and Technology, Ulan Bator, Mongolia
  • 2 Department of Economics, Other, Ulaanbaatar, Mongolia

The final, formatted version of the article will be published soon.

    We consider a continuous-time model of optimal consumption and pension insurance for a consumer with an uncertain lifetime. In the model, the consumer earns a stochastic wage income during her working life and optimally allocates her income between personal consumption, pension insurance, and securities with a deterministic dynamic return. Due to the weak development of the stock market in developing countries, employees' income comes mainly from wages and interest on savings from banks, that are discussed in this paper. The consumer's utility and bequest functions are CARA (constant absolute risk aversion). By characterizing the optimality condition of the consumer's problem using the Hamilton-Jacobi-Bellman equation, we find the optimal consumption and pension insurance as a function of wealth in closed form. We consider an application of the model while estimating its key elements using real-life data on age-specific population size, labour income, and interest rates. We show that as the absolute risk aversion for consumption increases, consumption and wealth move in the opposite direction. We also present a novel finding that wealth and consumption can be negatively related across consumers with different levels of consumption risk aversion.

    Keywords: stochastic optimal control, Optimal consumption, Pension insurance, Relative risk aversion, Bequest

    Received: 10 Apr 2024; Accepted: 19 Jul 2024.

    Copyright: © 2024 Terbish, Tserendorj, Dorj and Oirov. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Gereltuya Terbish, Mongolian University of Science and Technology, Ulan Bator, Mongolia

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