In this paper we apply a parametric semi-Markov pro\ud
cess to model the dynamic \ud
evolution of HIV-1 infected patients. The seriousne\ud
ss of the infection is rendered by the \ud
CD4+ T-lymphocyte counts. For this purpose we introd\ud
uce the main features of non-\ud
homogeneous semi-Markov models. After determining t\ud
he transition probabilities and \ud
the waiting time distributions in each state of the\ud
disease, we solve the evolution \ud
equations of the process in order to estimate the i\ud
nterval transition probabilities. These \ud
quantities appear to be of fundamental importance f\ud
or clinical predictions. We also \ud
estimate the survival probabilities for HIV infecte\ud
d patients and compare them with \ud
respect to certain categories, such as gender, age \ud
group or type of antiretroviral therapy. \ud
Finally we attach a reward structure to the aforeme\ud
ntioned semi-Markov processes in \ud
order to estimate clinical costs. For this purpose \ud
we generate random trajectories from \ud
the semi-Markov processes through Monte Carlo simul\ud
ation. The proposed model is \ud
then applied to a large database provided by ISS (I\ud
stituto Superiore di Sanità, Rome, \ud
Italy), and all the quantities of interest are comp\ud
uted
Disease progression models are useful tools for gaining a systems' understanding of the transitions to disease states, and characterizing the relationship between disease progress and factors affecting it such as patients' profile, treatment and the HIV diagnosis stage. Patients are classified into four states (based on CD4+ T-lymphocyte count) and all the transitions are allowed. Examinations to identify disease progression of the patient are carried out routinely throughout the follow-up period. Therefore, the times spent at the various HIV infection stages are interval censored or right censored. This makes difficult to use simple statistical methods such as regression to model the disease progression and its relationship with the diagnosis stage. We present a novel, more intuitive and realistic approach based on phase type distributions to model progression of HIV infection and the effects and prognostic significance of HIV diagnosis stage. The approach is illustrated using a real database of total 2,092 HIV infected patients enrolled in the Italian public structures from January 1996 to January 2008. The approach can also be used to examine the effect of other covariates such as patient's profile
We introduce the industrial portfolio of a wind farm of a hypothetical company and its valuation consistent with the financial market. Next, we propose a static risk management policy originating from hedging against volumetric risk due to drops in wind intensity and we discuss the consequences. The hedging effectiveness firstly requires adequate modeling calibration and an extensive knowledge of these atypical financial (commodity) markets. In this hedging experiment, we find significant benefits for weather-sensitive companies, which can lead to new business opportunities. We provide a new financial econometrics approach to derive weather risk exposure in a typical wind farm. Our results show how accurate risk management can have a real benefit on corporate revenues. Specifically, we apply the spot market price simulation (SMaPS) model for the spot price of electricity. The parameters are calibrated using the prices of the French day-ahead market, and the historical series of the total hourly load is used as the final consumption. Next, we analyze wind speed and its relationship with electricity spot prices. As our main contribution, we demonstrate the effects of a hypothetical hedging strategy with collar options implemented against volumetric risk to satisfy demand at a specific time. Regarding the hedged portfolio, we observe that the “worst value” increases considerably while the earnings-at-risk (EaR) decreases. We consider only volumetric risk management, thus neglecting the market risk associated with electricity price volatility, allowing us to conclude that the hedging operation of our industrial portfolio provides substantial benefits in terms of the worst-case scenario.
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