New stochastic processes to model interest rates : LIBOR additive processes

In this paper, a new kind of additive process is proposed. Our main goal is to define, characterize and prove the existence of the LIBOR additive process as a new stochastic process. This process will be de.ned as a piecewise stationary process with independent increments, continuous in probability but with discontinuous trajectories, and having "càdlàg" sample paths. The proposed process is specifically designed to derive interest-rates modelling because it allows us to introduce a jump-term structure as an increasing sequence of Lévy measures. In this paper we characterize this process as a Markovian process with an infinitely divisible, selfsimilar, stable and self-decomposable distribution. Also, we prove that the Lévy-Khintchine characteristic function and Lévy-Itô decomposition apply to this process. Additionally we develop a basic framework for density transformations. Finally, we show some examples of LIBOR additive processes

Credit risk with semimartingales and risk-neutrality

A no-arbitrage framework to model interest rates with credit risk, based on the LIBOR additive process, and an approach to price corporate bonds in incomplete markets, is presented in this paper. We derive the no-arbitrage conditions under different conditions of recovery, and we obtain new expressions in order to estimate the probabilities of default under risk-neutral measure

Credit risk with semimartingales and risk-neutrality

A no-arbitrage framework to model interest rates with credit risk, based on the LIBOR additive process, and an approach to price corporate bonds in incomplete markets, is presented in this paper. We derive the no-arbitrage conditions under different conditions of recovery, and we obtain new expressions in order to estimate the probabilities of default under risk-neutral measure.Credit-risk, Semimartingales, Interest-rate modelling

Weak convergence in credit risk

In the present paper, we study both the approximation of a continuous-time model by a sequence of discrete-time price models driven by semimargingales with credit risk, and the convergence of these price processes (in terms of the triplets) under a framework that allows the practitioner a multiple set of models (semimartingale) and credit conditions (migration and default)

LIBOR additive model calibration to swaptions markets

In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem. This problem can be splitted in the calibration of the continuous and discontinuous part, linking each part of the problem with at-the-money and in/out -of -the-money swaption volatilies. The continuous part is based on a semidefinite programming (convex) problem, with constraints in terms of variability or robustness, and the calibration of the Lévy measure is proposed to calibrate inverting the Fourier Transform

Weak convergence in credit risk

In the present paper, we study both the approximation of a continuous-time model by a sequence of discrete-time price models driven by semimargingales with credit risk, and the convergence of these price processes (in terms of the triplets) under a framework that allows the practitioner a multiple set of models (semimartingale) and credit conditions (migration and default).Weak convergence, Semimartingales, incomplete markets, Corporate bonds

LIBOR additive model calibration to swaptions markets

In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem. This problem can be splitted in the calibration of the continuous and discontinuous part, linking each part of the problem with at-the-money and in/out -of -the-money swaption volatilies. The continuous part is based on a semidefinite programming (convex) problem, with constraints in terms of variability or robustness, and the calibration of the Lévy measure is proposed to calibrate inverting the Fourier Transform.Lévy Market model, Calibration, Semidefinite programming

Time to Switch to Second-line Antiretroviral Therapy in Children With Human Immunodeficiency Virus in Europe and Thailand.

Background: Data on durability of first-line antiretroviral therapy (ART) in children with human immunodeficiency virus (HIV) are limited. We assessed time to switch to second-line therapy in 16 European countries and Thailand. Methods: Children aged <18 years initiating combination ART (≥2 nucleoside reverse transcriptase inhibitors [NRTIs] plus nonnucleoside reverse transcriptase inhibitor [NNRTI] or boosted protease inhibitor [PI]) were included. Switch to second-line was defined as (i) change across drug class (PI to NNRTI or vice versa) or within PI class plus change of ≥1 NRTI; (ii) change from single to dual PI; or (iii) addition of a new drug class. Cumulative incidence of switch was calculated with death and loss to follow-up as competing risks. Results: Of 3668 children included, median age at ART initiation was 6.1 (interquartile range (IQR), 1.7-10.5) years. Initial regimens were 32% PI based, 34% nevirapine (NVP) based, and 33% efavirenz based. Median duration of follow-up was 5.4 (IQR, 2.9-8.3) years. Cumulative incidence of switch at 5 years was 21% (95% confidence interval, 20%-23%), with significant regional variations. Median time to switch was 30 (IQR, 16-58) months; two-thirds of switches were related to treatment failure. In multivariable analysis, older age, severe immunosuppression and higher viral load (VL) at ART start, and NVP-based initial regimens were associated with increased risk of switch. Conclusions: One in 5 children switched to a second-line regimen by 5 years of ART, with two-thirds failure related. Advanced HIV, older age, and NVP-based regimens were associated with increased risk of switch

Prevalence and Clinical Outcomes of Poor Immune Response Despite Virologically Suppressive Antiretroviral Therapy Among Children and Adolescents With Human Immunodeficiency Virus in Europe and Thailand: Cohort Study

BACKGROUND: In human immunodeficiency virus (HIV)-positive adults, low CD4 cell counts despite fully suppressed HIV-1 RNA on antiretroviral therapy (ART) have been associated with increased risk of morbidity and mortality. We assessed the prevalence and outcomes of poor immune response (PIR) in children receiving suppressive ART. METHODS: Sixteen cohorts from the European Pregnancy and Paediatric HIV Cohort Collaboration (EPPICC) contributed data. Children &lt;18 years at ART initiation, with sustained viral suppression (VS) (≤400 copies/mL) for ≥1 year were included. The prevalence of PIR (defined as World Health Organization advanced/severe immunosuppression for age) at 1 year of VS was described. Factors associated with PIR were assessed using logistic regression. Rates of acquired immunodeficiency syndrome (AIDS) or death on suppressive ART were calculated by PIR status. RESULTS: Of 2318 children included, median age was 6.4 years and 68% had advanced/severe immunosuppression at ART initiation. At 1 year of VS, 12% had PIR. In multivariable analysis, PIR was associated with older age and worse immunological stage at ART start, hepatitis B coinfection, and residing in Thailand (all P ≤ .03). Rates of AIDS/death (95% confidence interval) per 100 000 person-years were 1052 (547, 2022) among PIR versus 261 (166, 409) among immune responders; rate ratio of 4.04 (1.83, 8.92; P &lt; .001). CONCLUSIONS: One in eight children in our cohort experienced PIR despite sustained VS. While the overall rate of AIDS/death was low, children with PIR had a 4-fold increase in risk of event as compared with immune responders