Monte Carlo Simulation in the Integrated Market and Credit Portfolio Model

Credit granting institutions deal with large portfolios of assets. These assets represent credit granted to obligors as well as investments in securities. A common size for such a portfolio lies from anywhere between 400 to 10,000 instruments. The essential goal of the credit institution is to minimize their losses due to default. By default we mean any event causing an asset to stop producing income. This can be the closure of a stock as well as the inability of an obligor to pay their debt, or even an obligor's decision to pay out all his debt. Minimizing the combined losses of a credit portfolio is not a deterministic problem with one clean solution. The large number of factors influencing each obligor, different market sectors, their interactions and trends, etc. are more commonly dealt with in terms of statistical measures. Such include the expectation of return and the volatility of each asset associated with a given time horizon. In this sense, we consider in the following the expected loss and risk associated with the assets in a credit portfolio over a given time horizon of (typically) 10 to 30 years. We use a Monte Carlo approach to simulate the loss of a portfolio in multiple scenarios, which leads to a distribution function for the expected loss of the portfolio over that time horizon. Second, we compare the results of the simulation to a Gaussian approximation obtained via the Lindeberg-Feller Theorem. Consistent with our expectations, the Gaussian approximation compares well with a Monte Carlo simulation in case of a portfolio of very risky assets. Using a model which produces a distribution of expected losses allows credit institutions to estimate their maximum expected loss with a certain confidence interval. This in turn helps in taking important decisions about whether to grant credit to an obligor, to exercise options or otherwise take advantage of sophisticated securities to minimize losses. Ultimately, this leads to the process of credit risk management

Singular perturbations of a boundary-value problem for a system of nonlinear differential equations

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The nonlinear boundary-value problem [...] is examined, under the hypothesis that the degenerate problem [...], has a continuously differentiable solution. Under a series of assumptions concerned, for the most part, with the smoothness of the functions f and g, it is proved that, for [...] restricted to a small enough interval of the form [...], the above boundary-value problem has a solution of the form [...], where p and q are both 0(1) uniformly in t as [...] goes to zero, while [...] and [...] exhibit a boundary-layer type of behavior

Nicholson’s blowflies equation with a distributed delay

on the occasion of their retirement ABSTRACT. For the Nicholson’s blowflies equation with a distributed delay Z t N(t) ˙ = −δN(t) + p N(s)e h(t) −aN(s) dsR(t, s), t ≥ 0, we obtain existence, positiveness and permanence results for solutions with positive initial conditions. We prove that all nonoscillatory about the positive equilibrium N ∗ solutions tend to N ∗. In the case δ < p < δe there are no slowly oscillating solutions and the positive equilibrium is globally asymptotically stable. Some generalizations to other nonlinear models of population dynamics with a distributed delay in the recruitment term and a nondelayed linear death term are considered

Beta-2 transferrin is detectable for 14 days whether refrigerated or stored at room temperature

BACKGROUND: The effect of time and temperature on beta-2 transferrin stability in cerebrospinal fluid (CSF) is not well established. After collecting nasal CSF for testing, beta-2 transferrin has been found to be stable and detectable for 1 week, whether being refrigerated or stored at room temperature. The purpose of this study was to determine if beta-2 transferrin remained detectable longer than 1 week and whether refrigeration improved its detectability. METHODS: In patients undergoing therapeutic CSF diversion, 2-mL CSF samples were collected from 18 patients. The samples were divided and stored either at room temperature, or at 4°C, and tested for beta-2 transferrin at 7 and 14 days. CSF was collected from external ventricular drains (EVDs) (n = 15), lumbar drains (n = 2), and subdural drains (n = 1). RESULTS: Of the 18 CSF samples originally testing positive for beta-2 transferrin, none turned negative at 7 or 14 days, in both the refrigerated and room temperature groups (95% confidence interval [CI], 0% to 18.5%). CONCLUSION: Beta-2 transferrin remained detectable for 14 days in all CSF samples, regardless of being stored at 4°C or room temperature

Beta-2 transferrin is detectable for 14 days whether refrigerated or stored at room temperature

BACKGROUND: The effect of time and temperature on beta-2 transferrin stability in cerebrospinal fluid (CSF) is not well established. After collecting nasal CSF for testing, beta-2 transferrin has been found to be stable and detectable for 1 week, whether being refrigerated or stored at room temperature. The purpose of this study was to determine if beta-2 transferrin remained detectable longer than 1 week and whether refrigeration improved its detectability. METHODS: In patients undergoing therapeutic CSF diversion, 2-mL CSF samples were collected from 18 patients. The samples were divided and stored either at room temperature, or at 4°C, and tested for beta-2 transferrin at 7 and 14 days. CSF was collected from external ventricular drains (EVDs) (n = 15), lumbar drains (n = 2), and subdural drains (n = 1). RESULTS: Of the 18 CSF samples originally testing positive for beta-2 transferrin, none turned negative at 7 or 14 days, in both the refrigerated and room temperature groups (95% confidence interval [CI], 0% to 18.5%). CONCLUSION: Beta-2 transferrin remained detectable for 14 days in all CSF samples, regardless of being stored at 4°C or room temperature

Beta-2 transferrin is detectable for 14 days whether refrigerated or stored at room temperature

BACKGROUND: The effect of time and temperature on beta-2 transferrin stability in cerebrospinal fluid (CSF) is not well established. After collecting nasal CSF for testing, beta-2 transferrin has been found to be stable and detectable for 1 week, whether being refrigerated or stored at room temperature. The purpose of this study was to determine if beta-2 transferrin remained detectable longer than 1 week and whether refrigeration improved its detectability. METHODS: In patients undergoing therapeutic CSF diversion, 2-mL CSF samples were collected from 18 patients. The samples were divided and stored either at room temperature, or at 4°C, and tested for beta-2 transferrin at 7 and 14 days. CSF was collected from external ventricular drains (EVDs) (n = 15), lumbar drains (n = 2), and subdural drains (n = 1). RESULTS: Of the 18 CSF samples originally testing positive for beta-2 transferrin, none turned negative at 7 or 14 days, in both the refrigerated and room temperature groups (95% confidence interval [CI], 0% to 18.5%). CONCLUSION: Beta-2 transferrin remained detectable for 14 days in all CSF samples, regardless of being stored at 4°C or room temperature

The Effect of Antithrombotics on Hematoma Expansion in Small- to Moderate-Sized Traumatic Intraparenchymal Hemorrhages

BACKGROUND: Although pre-injury antithrombotic agents, including antiplatelets and anticoagulants, are historically associated with expansion of traumatic intraparenchymal hemorrhage (tIPH), the literature has poorly elucidated the actual risk of hematoma expansion on repeat computed tomography (CT). The objective is to determine the effect of antithrombotic agents on hematoma expansion in tIPH by comparing patients with and without pre-injury antithrombotic medication. METHODS: The volume of all tIPHs over a 5-year period at an academic Level 1 Trauma Center was measured retrospectively. The initial tIPH was divided into three equally-sized quantiles. The third tertile, representing the largest subset of tIPH, was then removed from the study population because these patients reflect a different pathophysiological mechanism that may require a more acute and aggressive level of care with reversal agents and/or operative management. Per institutional policy, all patients with small- to moderate-sized hemorrhages received a 24-hour stability CT scan. Patients who received reversal agents were excluded. RESULTS: Of the 105 patients with a tIPH on the initial head CT scan, small- to moderate-size hemorrhages were \u3c5 cm(3). The size of tIPH on initial imaging did not statistically significantly differ between the antithrombotic cohort (0.7±0.1 cm(3)) and the non-antithrombotic cohort (0.5±0.1 cm(3)) (P=0.091). Similarly, the volume of tIPH failed to differ on 24-hour repeat imaging (1.0±0.2 cm(3) vs. 0.6±0.1 cm(3), respectively, P=0.172). Following a multiple linear regression, only history of stroke, not antithrombotic medications, predicted increased tIPH on 24-hour repeat imaging. CONCLUSION: In small- to moderate-sized tIPH, withholding antithrombotic agents without reversal may be sufficient