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Ergodicity transformation for additive-ruin wealth dynamic

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  • Carlos Rodríguez Raposo

    (OpSeeker Tech SL)

  • Pablo Coello Pulido

    (OpSeeker Tech SL)

Abstract

Ergodicity economics provides a framework to derive utility functions that assure growth optimality without entering into subjective or psychological considerations. For additive wealth dynamics the utility function is linear. This implies risk neutrality and contrasts with empirical evidence that shows risk aversion for decision makers. In this article we derive the utility function for the additive-ruin dynamic, which is a modified additive dynamic that includes a ruin state. As in ruin theory, we define a wealth level under which the agent is considered to be ruined. Furthermore, like in the model of parisian ruin, we consider the agent to be ruined as long as she does not recover with time. The obtained utility is a linear plus exponential function which has already been studied in economic theory. Unlike in the pure additive case, we show that ergodicity economics predicts risk averse behavior for agents in the additive-ruin dynamic. This result gives an explanation to why agents might refuse positive expected value lotteries for some levels of wealth and not for others without having to make subjective hypothesis about the agent.

Suggested Citation

  • Carlos Rodríguez Raposo & Pablo Coello Pulido, 2021. "Ergodicity transformation for additive-ruin wealth dynamic," Working Papers hal-03198073, HAL.
    • Handle: RePEc:hal:wpaper:hal-03198073
    Note: View the original document on HAL open archive server: https://hal.science/hal-03198073v3
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    References listed on IDEAS

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    Keywords

    ergodicity economics; utility function; additive dynamics; ruin theory;
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