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The game theoretic interpretation of gamblets is extended from Sobolev spacesto the Banach space setting. Identities for conditional covariances are presented in this generalized setting.
The minmax solution of the mixed extension of an optimal recovery game is evaluated in terms of the optimal recovery splines. Furthermore, the latter are given the interpretation of optimal bets in a mixed extension of the game corresponding to elementary components of the values of the measurement functions, giving rise to the interpretation of these optimal recovery splines as elementary bets, or gamblets. The screening effect is described and a rigorous proof of it established using exponential decay properties of the gamblets generated by Dirac delta measurement functions.
This study applies a multivariate model to examine the dynamics of mean and volatility transmission between fine wine and crude oil prices using daily observations from January 2004 to December 2011. The results suggest that the crude oil mean determines the wine market. In each series, volatility persistence is high and significant; innovations in each market seem to include figures that are valuable to risk managers seeking to predict volatility in other markets. During the financial crisis of 2008, wine and oil conditional volatilities climbed but then returned to their overall pre-crisis levels. (JEL Classifications: G11, G15, Q14, Q40)
A construction is given for a stationary sequence of random variables {Xi} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {εi}. The joint and trivariate exponential distributions of Xi−1, Xi and Xi+ 1 are studied, as well as the intensity function, point spectrum and variance time curve for the point process which has the {Xi} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higher-order moving averages and Gamma point processes are discussed.
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