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Dependence of Stock Returns in Bull and Bear Markets

Jadran Dobric, Gabriel Frahm, Friedrich Schmid (2013)

Dependence Modeling

Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns...

Discrete Lundberg-type bounds with actuarial applications

Kristina Sendova (2007)

ESAIM: Probability and Statistics

Different kinds of renewal equations repeatedly arise in connection with renewal risk models and variations. It is often appropriate to utilize bounds instead of the general solution to the renewal equation due to the inherent complexity. For this reason, as a first approach to construction of bounds we employ a general Lundberg-type methodology. Second, we focus specifically on exponential bounds which have the advantageous feature of being closely connected to the asymptotic behavior (for large...

Dynamic credibility with outliers and missing observations

Tomáš Cipra (1996)

Applications of Mathematics

In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the M -estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.

Dynamic model of market with uninformed market maker

Martin Šmíd, Miloš Kopa (2017)

Kybernetika

We model a market with multiple liquidity takers and a single market maker maximizing his discounted consumption while keeping a prescribed probability of bankruptcy. We show that, given this setting, spread and price bias (a difference between the midpoint- and the expected fair price) depend solely on the MM's inventory and his uncertainty concerning the fair price. Tested on ten-second data from ten US electronic markets, our model gives significant results with the price bias decreasing in the...

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