Diverse beliefs

Brown, A. A.; Rogers, L. C. G.

doi:10.1080/17442508.2012.656125

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…We introduce the information process {ξ t } defined by (2.6), along with the filtration {F t } that it generates, and we define the asset price by (2.7) and the pricing kernel by (3.4). By virtue of the relation dξ 2 t = dt, the dynamical equation satisfied by the asset price takes the form dS t = rS t dt + σ S t dξ t .…”

Section: Information-based Estimation Of Market Risk Aversionmentioning

confidence: 99%

“…Indeed, one can be overwhelmed by trying to contend with all the different types of heterogeneity that can arise in financial markets-heterogeneity in risk attitude, in impatience, in probability assignment, in transmission of information, in network connectivity, in information processing speed, and so on. See Brown & Rogers [2], Duffie [3], Ziegler [4], and references cited therein, for overviews of some of the issues connected to heterogeneity in financial markets currently being pursued. There is also a large literature devoted to portfolio management under partial information (see, for example, Björk et al [5] and references cited therein).…”

Section: Introductionmentioning

confidence: 99%

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Lévy information and the aggregation of risk aversion

Brody

Hughston

2013

Proc. R. Soc. A.

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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.

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Section: Information-based Estimation Of Market Risk Aversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lévy information and the aggregation of risk aversion

Brody

Hughston

2013

Proc. R. Soc. A.

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A Signal-Based Heterogeneous Agent Network

Aydın¹

2017

Financial Modelling With Forward-Looking Information

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The influence of financial practice in developing mathematical probability

Johnson

2020

Synthese

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The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a "mathematical mechanistic world picture" that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing (FTAP), the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument (DBA), the most popular justification for subjective probability. The paper's main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems.

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Diverse beliefs

Cited by 5 publications

References 34 publications

Lévy information and the aggregation of risk aversion

Lévy information and the aggregation of risk aversion

A Signal-Based Heterogeneous Agent Network

The influence of financial practice in developing mathematical probability

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