Interior-point algorithms for convex optimization based on primal-dual metrics

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity bounds for primal-dual symmetric interior-point algorithm of Nesterov and Todd, for symmetric cone programming problems with given self-scaled barriers. Our results apply to any self-concordant barrier for any convex cone. We also prove that certain specializations of our algorithms to hyperbolic cone programming problems (which lie strictly between symmetric cone programming and general convex optimization problems in terms of generality) can take advantage of the favourable special structure of hyperbolic barriers. We make new connections to Riemannian geometry, integrals over operator spaces, Gaussian quadrature, and strengthen the connection of our algorithms to quasi-Newton updates and hence first-order methods in general.Comment: 36 page

On the Pricing of Performance Sensitive Debt

Performance sensitive debt (PSD) contracts link a loan's interest rate to a measure of the borrower's credit relevant performance, e.g., if the borrower becomes less credit worthy, the interest rate increases according to a predetermined schedule. We derive and empirically test a pricing model for PSD contracts and find that interest increasing contracts are priced reflecting a substantial risk of shocks to borrower credit quality. Borrowers using such contracts are of an overall higher credit quality compared to borrowers using interest decreasing contracts. These contracts are priced as if no risk of shocks to borrower credit quality is present.Performance sensitive debt; cash flow ratios; credit ratings

Teoretisk og numerisk prising av korrelasjonsavhengige kredittderivater

Denne utredningen tar sikte på å studere og sammenligne ulike teoretiske modeller for prising av kredittderivater der underliggende aktivum er en portefølje av aktiva. Historiske data viser oss at konkurser har en tendens til å opptre uregelmessig og i klynger. Prisingsmodellene vi bruker for å prise slike kontrakter må derfor ta hensyn til denne korrelasjonsproblematikken på en tilfredsstillende måte. Viktig for oss er det også å vise hvordan disse modellene kan implementeres i praksis. Vi gjør dette gjennom å bruke relativt enkle numeriske eksempler. Vi starter oppgaven med å gi en generell oversikt over hva begrepet kredittrisiko er, og hvordan denne risikoen måles i praksis. Vi gir så en oversikt over hvilke produkter som er sentrale i dagens kredittderivatmarked, og beskriver hvordan strukturen i disse produktene er bygd opp. Videre følger en mer teoretisk del, der vi først presenterer to hovedtyper av kredittrisikomodeller; strukturerte modeller og redusert form modeller. Disse modellene danner selve fundamentet for de mer spesifikke modellene vi studerer senere i oppgaven. Konkurskorrelasjoner er, sammen med individuelle konkurssannsynligheter og andel tilbakebetalt ved konkurs, den viktigste faktoren i prising av korrelasjonsavhengige kredittderivater. Etter en kort forklaring på hvordan de to første faktorene kan estimeres går vi videre med å beskrive hva korrelasjoner er og hvordan man kan estimere disse. Siste del av oppgaven blir viet til en studie av flere ulike modeller som hver har sine måter å løse korrelasjonsproblematikken på. Vi fokuserer i hovedsak på modeller med solide teoretiske fundament, men inkluderer også en praktisk tilnærming til problemet. Styrkene og svakhetene til de ulike modellene blir kommentert

Hva predikerer ytelsene til en offiser? En evaluering av seleksjon til Forsvarests befalskoler

I denne studien har jeg undersøkt hva som predikerer ytelsene til en offiser. Det ble valgt prediktorer fra Felles Opptak og Seleksjon (FOS) for befalskolene som benyttes ved dagens seleksjonsprosess og to nye prediktorer; self-efficacy og hardiness som ikke benyttes til seleksjon, men som i andre studier har vist å ha betydning for prestasjoner. Prediktorene ble målt opp mot kriteriet hovedkarakter fra befalsskolene og Skikkethet Militær Leder (SML) fra tjenesteuttalelsen. Utvalget i studien (N = 417) var alle som gikk befalsskole i Forsvaret i 2015. Den prediktive validiteten til prediktorene ble undersøkt gjennom korrelasjons- og stegvis regresjonsanalyse for å avdekke i hvilken grad prediktorene forklarte varians i de to kriteriene som var hovedkarakter og skikkethet militær leder, og om self-efficacy og hardiness bidro med ytterligere forklart varians i forhold til de prediktorene som allerede anvendes i seleksjonsprosessen. Funnene i studien viste at Allment Evnenivå (AE) og skolepoeng predikerte hovedkarakter (r = .26 og r = .31), mens offisersvurdering (feltuke) predikete «skikkethet militær leder» (r = .24). Self-efficacy og hardiness predikerte hverken hovedkarakter eller skikkethet militær leder. Dette illustrerte at prediktorene som ble benyttet ved FOS var hensiktsmessig i forhold til å predikere resultater i form av hovedkarakter og skikkethet militær leder.This study examines if it is possible to predict an military officer’s performance. Specific abilities and aptitudes were chosen from data recorded during the officer candidate school selection process. These previously recorded characteristics were examined together with two new potential predictors; “self-efficacy” and “hardiness.” While these are not used in the normal selection process, other studies have shown that they are related to performance. The predictors were correlated with two performance criteria “Grade Point Average” (GPA) and “suitability as a military leader” (SML). The study sample (N=417) included all individuals that graduated from officer candidate school in the Norwegian armed forces 2015. To estimate the predictive validity of the selection system and the potential incremental validity of the two new predictors (self-efficacy and hardiness), correlations and stepwise regression analyses were conducted in order to examine to what extent they explained the variance in “grade point average” and “suitability as a military leader.” The findings from this study indicated that “general mental ability” and “grade point average” (from upper secondary school) predicted “grade point average” (r = .26 and r = .31), while “assesment as officer” (assess during field training) predicted “suitability as a military leader” (r = .24). Neither self-efficacy or hardiness predicted “grade point average” or “suitability as a military leader” or contributed to incremental validity in the regression analyses. This indicates that the existing predictors currently utilized for officer assession are suitable to predict an officer’s performance regarding “grade point average” and “suitability as a military leader”

Geometry of convex sets arising from hyperbolic polynomials

This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials. We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning polynomials in a single variable, as well as presenting a few more modern results about them. We then discuss the theory of hyperbolic polynomials in several variables and their associated hyperbolicity cones. We survey various ways to build and decompose hyperbolic cones and we prove that every nontrivial hyperbolic cone is the intersection of its derivative cones. We conclude with a brief discussion of the set of extreme rays of a hyperbolic cone

Data Safety, Sources, and Data Flow in the Offshore Industry

Digitization may provide increased access to and more efficient use of real-time and historical data, internally as well as externally in an organization. However, when information from industrial control systems (ICS) becomes more available in office IT systems and in the "cloud", ICS systems may become more vulnerable and attractive targets for cyberattacks. We have investigated data safety in ICS in the Norwegian offshore sector when data is processed from ICS to the office network. The work is mainly based on document review and nine interviews with selected oil companies, rig companies and service providers of operational data. The paper addresses strengths and threats related to data safety with emphasis on (1) Data sources and data flow, (2) Safety and security of data, (3) Data cleaning and processing, (4) Contextualization, (5) Validation, and (6) Quality assurance. We also discuss shortcomings for functional safety in current standards such as IEC 61508 and IEC 61511 and standard series for security, IEC 62443. It is a major challenge for the industry that there are no good international standards and guidelines that define the relevant terminology across IT systems and ICS. Future work should address data safety challenges when applying artificial intelligence and machine learning in ICS systems.publishedVersio

Treatment and survival of patients with pancreatic ductal adenocarcinoma: 15-year national cohort

Background - Improvement in survival from pancreatic ductal adenocarcinoma (PDAC) has been reported in trial settings but is less explored in unselected cohorts. The aim of this study was to assess trends in provision of treatments and survival in Norway over a 15-year period following the implementation of hepato-pancreato-biliary (HPB) multidisciplinary teams, centralization of surgery, and implementation of modern chemotherapy (CTx) regimens. Methods - A population-based observational study was conducted by analysing all patients diagnosed with PDAC between 2004 and 2018 using coupled data from the Cancer Registry of Norway and the National Patient Registry. Results - A total of 10 630 patients were identified, of whom 1492 (14.0 per cent) underwent surgical resection. The resection rate, median age of those resected, and provision of perioperative CTx all increased over time. Median overall survival after resection improved from 16.0 months in the period 2004 to 2008 to 25.1 months in the period 2014 to 2018 (P  Conclusion - Survival after resection increased substantially, as did national resection rates. Little development in the provision of CTx or survival was observed for non-resected patients

Accurate population-based model for individual prediction of colon cancer recurrence

Background Prediction models are useful tools in the clinical management of colon cancer patients, particularly when estimating the recurrence rate and, thus, the need for adjuvant treatment. However, the most used models (MSKCC, ACCENT) are based on several decades-old patient series from clinical trials, likely overestimating the current risk of recurrence, especially in low-risk groups, as outcomes have improved over time. The aim was to develop and validate an updated model for the prediction of recurrence within 5 years after surgery using routinely collected clinicopathologic variables. Material and methods A population-based cohort from the Swedish Colorectal Cancer Registry of 16,134 stage I–III colon cancer cases was used. A multivariable model was constructed using Cox proportional hazards regression. Three-quarters of the cases were used for model development and one quarter for internal validation. External validation was performed using 12,769 stage II–III patients from the Norwegian Colorectal Cancer Registry. The model was compared to previous nomograms. Results The nomogram consisted of eight variables: sex, sidedness, pT-substages, number of positive and found lymph nodes, emergency surgery, lymphovascular and perineural invasion. The area under the curve (AUC) was 0.78 in the model, 0.76 in internal validation, and 0.70 in external validation. The model calibrated well, especially in low-risk patients, and performed better than existing nomograms in the Swedish registry data. The new nomogram’s AUC was equal to that of the MSKCC but the calibration was better. Conclusion The nomogram based on recently operated patients from a population registry predicts recurrence risk more accurately than previous nomograms. It performs best in the low-risk groups where the risk-benefit ratio of adjuvant treatment is debatable and the need for an accurate prediction model is the largest.publishedVersio