We introduce the expectation of a random variable on a probability space, which is its best guess in the least-squares sense. The variance is an operator quantifying the dispersion of its distribution. We recall the expression of the expectation and variance of a weighted sum of variables. The moment generating function is a characterization of a distribution which is powerful for finding the distribution of a linear combination of variables. Those concepts are then extended to pairs of variables, for which covariance and correlation can be defined. The Central Limit Theorem gives another interpretation to the expectation, which is also the asymptotic value taken by the average of variables having the same distribution. Finally, we introduce a special class of random variables called Radon–Nikodym derivatives, which are nonnegative and display unit expectation. This family of variables can be used to build new probability measures starting from a reference probability space. Switching probability measures triggers a modification of the distribution of the random variables at hand. Those concepts are illustrated on various examples including coins, dice, and stock price models.

A general practice nurse is a registered or enrolled nurse employed in a primary care (general practice) setting. Approximately 82 000 nurses are working outside of hospital settings in Australia and two-thirds (68 per cent) of these work in general practice. It is estimated that over 90 per cent of general practices employ nurses. Aotearoa New Zealand workforce data reveals that in 2018–19, 5.5 per cent of the total nursing workforce worked in general practice, accounting for some 3018 nurses. This places general practice as one of the ten largest practice areas within the Aotearoa New Zealand nursing workforce.

A masters-level overview of the mathematical concepts needed to master the art of derivatives pricing, this textbook is a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, the book allows students with limited technical background to build a solid knowledge base of the most important notions. It offers a unique compromise between intuition and mathematics, even when discussing abstract notions such as change of measure. Mathematical concepts are initially introduced using “toy” examples, before moving on to examples of finance cases, in both discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students’ understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code, and an interactive app.

This chapter discusses some improvements to the Black–Scholes–Merton model. In practice, the stock price does not follow a GBM (log-returns exhibit fat tails) and volatility tends to increase when the stock price decreases (leverage effect). Although not captured by the BSM model, those effects are priced. This is evidenced by the implied volatility surface. The implied volatility of a given option is the value of the volatility parameter one needs to insert in the BSM formula to match the market price of this option. The fact that the implied volatility depends not only on the asset but also on the characteristics of the option (such as the strike or expiry) contradicts the BSM model. More realistic setups can be designed to capture those effects. This is the case of the Heston model, which exhibits the fat-tail feature, the leverage effect, and the curved implied volatility surface. Another important assumption inherent to the plain BSM model is that the payoff will be paid in every circumstances. This is clearly not the case because any counterparty is exposed to bankruptcy risk. This calls for an adjustment to the risk-free price known as credit valuation adjustment (CVA).

Community and primary health care nursing is experiencing a rapid metamorphosis as our population ages and the prevalence of chronic and complex conditions increases. To meet these changing needs, our health workforce has evolved with a range of specialised disciplines now working in diverse health settings. Throughout these changes, nursing continues to be the largest global health workforce providing the most direct client care. Historically, nurses were the original transdisciplinary health care workers, providing basic physiotherapy, occupational therapy, nutritional advice and all other care as required. As more detailed knowledge developed in an area of practice, specialised areas of care evolved, and a variety of allied health professions emerged. In turn, nursing itself became more specialised, due to developments in clinical practice, technological advances and the need for more complex care.

This chapter focuses on the theory, skills and professional role of a drug and alcohol nurse in community settings. It describes substance use and drug-related harms and provides a brief overview of the guiding principles and professional practice drug and alcohol nurses follow when providing care for people who use alcohol and other drugs (AOD). The chapter also describes the considerations for co-occurring needs and integrated care. Reflective activities throughout the chapter will guide the reader to consider how they can support people living with AOD in their nursing practice.

The world is facing an unprecedented number of forcibly displaced people as a result of war, conflict, human rights violations and natural disasters. Conflicts have become more protracted, often lasting for years, and displacement as a short-term option is unrealistic. The most recent United Nations High Commissioner for Refugees (UNHCR) annual global trends report shows an ever-increasing number of people displaced. The UNHCR has estimated it will be supporting an expected 130 million people who are either stateless or forcibly displaced by the end of 2024. Around half of the world’s refugees and displaced people are children. Permanent resettlement is no solution as less than 1 per cent of the displaced people are ever resettled.

The World Health Organization developed a framework for family and community nursing that identified a role for community health nurses, identifying the needs of their communities and addressing them. Primary health care shifted the focus from a disease model treating illness to a preventative model that focused on population and social health, community development, health promotion, illness prevention and early intervention, including community nurses as part of this movement.

We study the application of the Cox-–Ross–Rubinstein model to pricing financial contracts. The determination of the “fair price” consists in looking for an adapted self-financing trading strategy replicating the payoff of the product at hand, and determining the amount needed to launch this procedure. We observe that the mathematical expression of this price takes the form of the conditional expectation of the payoff discounted at the risk-free rate provided that one considers a specific set of probabilities when computing the expectation. This amounts to computing the expectation under a special probability measure (called risk-neutral measure) equivalent to – but different from – the physical probability measure. We show that the risk-neutral measure has the specific property that the price process of assets paying no cashflows are martingales when discounted at the risk-free rate. We illustrate using zero-coupon bonds, forward contracts, and European options that the price found by computing the risk-neutral expectation indeed enables us to start a self-financing strategy that replicates the payoff of those products on a binomial tree.

Cultural competence and cultural safety support health professionals to recognise everyone as unique in order to promote optimal health outcomes. This allows for the acknowledgement of diversity that exists within and between individuals and groups in health care. In practice, this represents the broader understanding of culture in health care, and encompasses the dynamic influences of culture on attitudes, values and beliefs. Alongside culture, the understanding of diversity is inclusive of – yet not exclusive to – age and generation, sex and gender identity, socio-economic status, occupation, ethnicity or migrant experience, religion or spirituality, and ability or disability.

We derive a deterministic equation whose solution yields the expression of the no-arbitrage price of a derivative security in continuous time. In contrast to Chapter 11 where the latter is found via a risk-neutral expectation, we adopt a no-arbitrage argument as in Chapter 15. To this end, we look for a trading strategy that would (i) be self-financing, (ii) comply with the evolution of a function which only depends on time and on the current price of the underlying asset, and (ii) replicate the derivative’s payoff. Solving this problem yields (i) a partial differential equation (PDE) whose solution is the price function and (ii) the analytical expression of the replicating strategy, something that we failed to obtain in Chapter 11. We show that the price of ZCBs, forward contracts and European call and put options computed using risk-neutral expectations all satisfy the PDE. The price of a specific product is determined by picking the price function that complies with its payoff. The Feynman–Kac theorem justifies that the price found using the risk-neutral expectation approach in Chapter 11 coincides with the no-arbitrage expression obtained by following a replication argument.

Event studies are commonly applied in corporate finance, with a focus on testing market efficiency hypotheses and evaluating the effects of corporate decisions on firm values, stock prices, and other outcome variables. The chapter discusses the event-study model using examples from (i) return predictability literature; (ii) the effects of firm-level and macro news on stock returns, testing semi-strong efficiency; as well as (iii) insider trading, testing the strong form of efficiency. In short-term event studies the chapter reviews abnormal (AR) and cumulative abnormal return (CAR) calculations and discusses statistical tests of ARs and CARs. It also covers long-term event studies and discusses the buy-and-hold abnormal returns as well as the calendar-time portfolio approach. The chapter provides an application of a short-term event study by examining how stock prices respond to the news of a CEO’s departure. The chapter ends with lab work and a mini case study.

A masters-level overview of the mathematical concepts needed to master the art of derivatives pricing, this textbook is a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, the book allows students with limited technical background to build a solid knowledge base of the most important notions. It offers a unique compromise between intuition and mathematics, even when discussing abstract notions such as change of measure. Mathematical concepts are initially introduced using “toy” examples, before moving on to examples of finance cases, in both discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students’ understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code, and an interactive app.