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If You’re So Smart, Why Aren’t You Rich? Belief Selection in Complete and Incomplete Markets
, 2001
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Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
, 2008
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Probabilistic bounds on the coefficients of polynomials with only real zeros
 J. Combin. Theory Ser. A
, 1997
"... The work of Harper and subsequent authors has shown that nite sequences (a 0;;an) arising from combinatorial problems are often such that the polynomial A(z): = P n k=0 akz k has only real zeros. Basic examples include rows from the arrays of binomial coe cients, Stirling numbers of the rst and sec ..."
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The work of Harper and subsequent authors has shown that nite sequences (a 0;;an) arising from combinatorial problems are often such that the polynomial A(z): = P n k=0 akz k has only real zeros. Basic examples include rows from the arrays of binomial coe cients, Stirling numbers of the rst and second kinds, and Eulerian numbers. Assuming the ak are nonnegative, A(1)> 0 and that A(z) is not constant, it is known that A(z) has only real zeros i the normalized sequence (a 0=A(1);;an=A(1)) is the probability distribution of the Research supported in part by N.S.F. Grant MCS9404345 1 number of successes in n independent trials for some sequence of success probabilities. Such sequences (a 0;;an) are also known to be characterized by total positivity of the in nite matrix (ai,j) indexed by nonnegative integers i and j. This papers reviews inequalities and approximations for such sequences, called Polya frequency sequences which follow from their probabilistic representation. In combinatorial examples these inequalities yield a number of improvements of known estimates.
The swine flu vaccine and GuillainBarré syndrome: a case study in relative risk and specific causation
 Evaluation Review
, 1999
"... Epidemiologic methods were developed to prove general causation: identifying exposures that increase the risk of particular diseases. Courts often are more interested in specific causation: on balance of probabilities, was the plainti#'s disease caused by exposure to the agent in quest ..."
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Cited by 5 (1 self)
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<F4.554e+05> Epidemiologic methods were developed to prove general causation: identifying exposures that increase the risk of particular diseases. Courts often are more interested in specific causation: on balance of probabilities, was the plainti#'s disease caused by exposure to the agent in question? Some authorities have suggested that a relative risk greater than 2.0 meets the standard of proof for specific causation. Such a definite criterion is appealing, but there are di#culties. Bias and confounding are familiar problems; individual di#erences must be considered too. The issues are explored in the context of the swine flu vaccine and GuillainBarre syndrome. The conclusion: there is a considerable gap between relative risks and proof of specific causation.<F4.051e+05> 1. Introduction<F4.554e+05> In a toxic tort case, the plainti# is exposed to a toxic agent, su#ers injury, and sues. To win, the plainti# must prove (i) "general causation" (the agent is capable of producing th...
The dynamics of efficient asset trading with Heterogeneous Beliefs
 J. ECON. THEORY
, 2010
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INVARIANCE THEOREMS FOR CENTERED SEQUENCES NORMED BY SUMS OF SQUARES by
, 1977
"... Let (Q,B,P) be a probability space supporting an increasing sequence of sigmafields {B} and a sequence of random variables {f} where f n n n is ..."
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Let (Q,B,P) be a probability space supporting an increasing sequence of sigmafields {B} and a sequence of random variables {f} where f n n n is
The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs
, 2009
"... This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibria when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and signi…cant ‡uctuations in individual portfolios may be c ..."
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This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibria when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and signi…cant ‡uctuations in individual portfolios may be correct but it also needs some quali…cations. We consider an in…nite horizon stochastic endowment economy where the actual process of the states of nature consists in i.i.d. draws. The economy is populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying portfolios that support Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents know that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the support of every agent’s prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.
Correspondence To:
, 2009
"... We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent’s equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then pro ..."
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We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent’s equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent’s consumption is bounded away from zero eventually, the other agent’s consumption is zero eventually–so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finitestatetimehomogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent’s consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) and Blume and Easley (2006) where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.
SELFNORMALIZED PROCESSES: EXPONENTIAL INEQUALITIES, MOMENT BOUNDS AND ITERATED LOGARITHM LAWS
, 2002
"... Selfnormalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, selfnormalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those relate ..."
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Selfnormalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, selfnormalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for selfnormalized random variables including martingales. Tail probability bounds are also derived. For random variables Bt> 0 and At, let Yt(λ) = exp{λAt − λ 2 B 2 t /2}. We develop inequalities for the moments of At/Bt or supt≥0 At/{Bt(loglog Bt) 1/2} and variants thereof, when EYt(λ) ≤ 1 or when Yt(λ) is a supermartingale, for all λ belonging to some interval. Our results are valid for a wide class of random processes including continuous martingales with At = Mt and Bt = √ 〈M〉t, and sums of conditionally symmetric variables di with ∑t