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On increasing risk, inequality and poverty measures: Peacocks, lyrebirds and exotic options

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  • Ewald, Christian-Oliver
  • Yor, Marc

Abstract

We extend the Rothschild and Stiglitz (1970) notion of increasing risk to families of random variables and in this way link their approach to the concept of stochastic processes which are increasing in the convex order. These processes have been introduced in seminal work by Strassen (1965), Doob (1968) and Kellerer (1972), who showed that such processes have the same marginals as a martingale. In fact, we demonstrate that their results include the results of Rothschild and Stiglitz as a special case. Further, we show that it makes sense to look at a larger class of processes, which we refer to as lyrebirds. We also show how these processes link up with the concept of second order stochastic dominance and are helpful in studying the dynamics of inequality and poverty measures. Further applications discussed include geometric and hyperbolic discounting, exotic derivatives and real options.

Suggested Citation

  • Ewald, Christian-Oliver & Yor, Marc, 2015. "On increasing risk, inequality and poverty measures: Peacocks, lyrebirds and exotic options," Journal of Economic Dynamics and Control, Elsevier, vol. 59(C), pages 22-36.
    • Handle: RePEc:eee:dyncon:v:59:y:2015:i:c:p:22-36
    DOI: 10.1016/j.jedc.2015.07.004
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    References listed on IDEAS

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    Cited by:

    1. Guglielmo D'Amico & Riccardo De Blasis & Philippe Regnault, 2020. "Confidence sets for dynamic poverty indexes," Papers 2006.06595, arXiv.org.
    2. Bogso, Antoine-Marie & Takam Soh, Patrice, 2017. "Weak decreasing stochastic order," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 49-58.
    3. Gabriela Pesce & Florencia Verónica Pedroni & Etelvina Chávez & María de la Paz Moral & María Andrea Rivero, 2021. "Exotic options: conceptualization and evolution in the literature from a systematic review," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 95, pages 231-275, July-Dece.
    4. Liu, Yating & Pagès, Gilles, 2022. "Monotone convex order for the McKean–Vlasov processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 312-338.

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    More about this item

    Keywords

    Increasing risk; Inequality; Poverty measures; Peacocks;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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