lévy subordinators
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2020 ◽  
Vol 8 (1) ◽  
pp. 210-220
Author(s):  
Jan-Frederik Mai

AbstractWe derive a sufficient condition on the symmetric norm ||·|| such that the probability distribution associated with the density function f (x) ∝exp(−λ ||x||) is conditionally independent and identically distributed in the sense of de Finetti’s seminal theorem. The criterion is mild enough to comprise the ℓp-norms as special cases, in which f is shown to correspond to a polynomially tilted stable mixture of products of transformed Gamma densities. In another special case of interest f equals the density of a time-homogeneous load sharing model, popular in reliability theory, whose motivation is a priori unrelated to the concept of conditional independence. The de Finetti structure reveals a surprising link between time-homogeneous load sharing models and the concept of Lévy subordinators.


2020 ◽  
Vol 11 (2) ◽  
pp. 535-577 ◽  
Author(s):  
Ruixuan Liu

This paper proposes a new bivariate competing risks model in which both durations are the first passage times of dependent Lévy subordinators with exponential thresholds and multiplicative covariates effects. Our specification extends the mixed proportional hazards model, as it allows for the time‐varying heterogeneity represented by the unobservable Lévy processes and it generates the simultaneous termination of both durations with positive probability. We obtain nonparametric identification of all model primitives given competing risks data. A flexible semiparametric estimation procedure is provided and illustrated through the analysis of a real dataset.


2019 ◽  
Vol 17 (3) ◽  
pp. 781-816 ◽  
Author(s):  
Denis Belomestny ◽  
Shota Gugushvili ◽  
Moritz Schauer ◽  
Peter Spreij

2018 ◽  
Vol 32 (4) ◽  
pp. 1909-1924
Author(s):  
Jan Schneider ◽  
Roman Urban

2010 ◽  
Vol 101 (6) ◽  
pp. 1428-1433 ◽  
Author(s):  
Christian Hering ◽  
Marius Hofert ◽  
Jan-Frederik Mai ◽  
Matthias Scherer

2009 ◽  
Vol 12 (02) ◽  
pp. 227-249 ◽  
Author(s):  
JAN-FREDERIK MAI ◽  
MATTHIAS SCHERER

A stochastic time-change is applied to introduce dependence to a portfolio of credit-risky assets whose default times are modeled as random variables with arbitrary distribution. The dependence structure of the vector of default times is completely separated from its marginal default probabilities, making the model analytically tractable. This separation is achieved by restricting the time-change to suitable Lévy subordinators which preserve the marginal distributions. Jump times of the Lévy subordinator are interpreted as times of excess default clustering. Relevant for practical implementations is that the parameters of the time-change allow for an intuitive economical explanation and can be calibrated independently of the marginal default probabilities. On a theoretical level, a so-called time normalization allows to compute the resulting copula of the default times. Moreover, the exact portfolio-loss distribution and an approximation for large portfolios under a homogeneous portfolio assumption are derived. Given these results, the pricing of complex portfolio derivatives is possible in closed-form. Three different implementations of the model are proposed, including a compound Poisson subordinator, a Gamma subordinator, and an Inverse Gaussian subordinator. Using two parameters to adjust the dependence structure in each case, the model is capable of capturing the full range of dependence patterns from independence to complete comonotonicity. A simultaneous calibration to portfolio-CDS spreads and CDO tranche spreads is carried out to demonstrate the model's applicability.


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