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Lévy information and the aggregation of risk aversion

In: Financial Informatics An Information-Based Approach to Asset Pricing

Author

Listed:
  • Dorje C. Brody
  • Lane P. Hughston

Abstract

When investors have heterogeneous attitudes towards risk, it is reasonable to assume that each investor has a pricing kernel, and that these individual pricing kernels are aggregated to form a market pricing kernel. The various investors are then buyers or sellers depending on how their individual pricing kernels compare with that of the market. In Brownian-based models, we can represent such heterogeneous attitudes by letting the market price of risk be a random variable, the distribution of which corresponds to the variability of attitude across the market. If the flow of market information is determined by the movements of prices, then neither the Brownian driver nor the market price of risk are directly visible: the filtration is generated by an ‘information process’ given by a combination of the two. We show that the market pricing kernel is then given by the harmonic mean of the individual pricing kernels associated with the various market participants. Remarkably, with an appropriate definition of Lévy information one draws the same conclusion in the case when asset prices can jump. As a consequence, we are led to a rather general scheme for the management of investments in heterogeneous markets subject to jump risk.

Suggested Citation

  • Dorje C. Brody & Lane P. Hughston, 2022. "Lévy information and the aggregation of risk aversion," World Scientific Book Chapters, in: Dorje Brody & Lane Hughston & Andrea Macrina (ed.), Financial Informatics An Information-Based Approach to Asset Pricing, chapter 10, pages 195-213, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789811246494_0010
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    Keywords

    Financial Mathematics; Mathematical Finance; Financial Markets; Informatics; Asset Pricing; Asset Price Dynamics; Stochastic Modelling; Information Process; Information Flow; Signal Processing; Filtration; Brownian Motion; Brownian Bridge; Change of Measure; Stochastic Volatility; Credit Risk; Default; Equities; Bonds; Collateralized Debt Obligation; Discount Bond; Lévy Process; Lévy Random Bridge; Lévy Information; Gamma Bridge; Markov Bridge; Pricing Kernel; Option Pricing; Informed Traders; Insurance; Reinsurance; Insurance Claims; Bond Portfolio; Heat Kernel; Markov Process; Variance Gamma Process; Ornstein-Uhlenbeck Process; Commodities; Fake News;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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