Subadditive Probabilities and Portfolio Inertia

Simonsen, Mário Henrique; Werlang, Sérgio Ribeiro da Costa

doi:10.12660/bre.v11n11991.3007

Cited by 20 publications

(14 citation statements)

References 7 publications

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“…These data are the first direct evidence that increasing ambiguity shifts measured attention from good outcomes to bad outcomes, providing a psychological underpinning to theories in which ambiguous probabilities of bad outcomes are overweighted, or a maximin SEU is calculated over pessimistic probabilities. Dow and Werlang (in press) applied SEU with nonadditive probability to asset markets 32 (see also Simonsen and Werlang, 1990). Consider an ambiguity-averse trader who begins owning no shares of a stock.…”

Section: Marketingmentioning

confidence: 99%

Recent developments in modeling preferences: Uncertainty and ambiguity

1992

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In subjective expected utility (SEU), the decision weights people attach to events are their beliefs about the likelihood of events. Much empirical evidence, inspired by Ellsberg (1961) and others, shows that people prefer to bet on events they know more about, even when their beliefs are held constant. (They are averse to ambiguity, or uncertainty about probability.) We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU.In the last 40 years the leading theories of choice in economics and psychology have been the expected utility (EU) theory of von Neumann and Morgenstern (1947) and the subjective expected utility (SEU) theory of Savage (1954). Empirical violations have led to reexaminations of both kinds of theory. In Weber and Camerer (1987), we reviewed the evidence, axioms, and application of alternatives to EU. Here we do the same for SEU.EU assumes that the probabilities of outcomes are known. If preferences follow a set of simple axioms, they can be represented by a real-valued utility function--preferred choices have higher utility numbers--and the utility of a choice is the expected utility of its possible outcomes, weighted by their probabilities.In SEU, probabilities are not necessarily objectively known, so SEU applies more widely than EU. (Indeed, it is hard to think of an important natural decision for which probabilities are objectively known.) In SEU, decision makers choose acts, which have consequences that depend on which of several uncertain "states" occurs. People are *Thanks to

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Section: Marketingmentioning

confidence: 99%

Recent developments in modeling preferences: Uncertainty and ambiguity

1992

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“…Among others, Dow and Werlang ( [21]) and Simonsen and Werlang ( [51]) considered models of portfolio optimization where agents are uncertain about the true probability measure. Their investors maximize their utility with respect to nonadditive probability measures.…”

Section: Inertia In Financial Marketsmentioning

confidence: 99%

A Limit Theorem for Financial Markets with Inert Investors

2006

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We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process with long range dependence and nonGaussian returns distributions, driven by a fractional Brownian motion. Consequently, investor inertia may lead to arbitrage opportunities for sophisticated market participants. The mathematical contributions are a functional central limit theorem for stationary semi-Markov processes, and approximation results for stochastic integrals of continuous semimartingales with respect to fractional Brownian motion.

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“…Clearly strong independence implies independence: in fact for S � X let S = {U E Ax : U � S} �and analogously do for T ) and substitute it in (36), so that (35) is obtained. If instead we take S = {S} and T = {T} we get…”

Section: Multi-valued Functions)mentioning

confidence: 99%

On Independence for Non-Additive Measures, with a Fubini Theorem

Ghirardato

1997

Journal of Economic Theory

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Recent models of decision making represent agents' beliefs by non-additive set-f unctions. An important technical question which arises in applications to diverse aereas of eco nomics is how to define independence of such set-functions. After arguing that the straightforward generalization of independence does not in general yield a unique prod uct, in this work I show that, while Fubini's theorem is in general false if additivity is not granted, it is true when a certain type of function is being integrated. For these functions the iterated integrals coincide with the integral with respect to products which satisfy a certain property, strictly stronger than independence. I show that most of the assumptions made in these results are very close to being necessary. In general the men tioned property is still not strong enough to uniquely define a product. On the other hand I discuss some proposals which have been made in the literature, and I show that u_ nicity can however be obtained when the product is assumed to be a belief function. Moreover I show that the unique product thus obtained has an intuitive justification when the marginals are distributions indu . ced by random correspondences. Finally I use the results in the paper to discuss the question of randomization in decision models with non-additive beliefs.

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Subadditive Probabilities and Portfolio Inertia

Cited by 20 publications

References 7 publications

Recent developments in modeling preferences: Uncertainty and ambiguity

Recent developments in modeling preferences: Uncertainty and ambiguity

A Limit Theorem for Financial Markets with Inert Investors

On Independence for Non-Additive Measures, with a Fubini Theorem

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