The role of occupational health nurses is to improve mental and physical health outcomes and the well-being of workers. These benefits can often extend to family and community. Workers’ health is impacted by several factors including fatigue, gender, culture, age, language, living conditions, access to nutritious food, level of physical activity, sleep patterns, personal health practices and coping strategies, levels of social support and inclusion, personal safety and freedom from violence.

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.

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.

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.

The evolution of the value of a trading strategy in discrete time is a weighted sum of quantities scaled by the change in the assets' value. The limit as the time-step tends to zero yields a continuous-time process taking the form of a sum of integrals of a process (number of shares) with respect to another (asset's price). This is a stochastic integral. Having recalled well-known Riemann integrals, we introduce the Riemann–Stieltjes extension and recall that their value can be estimated arbitrarily well using a finite sum. We introduce the differential of a process, and of a stochastic integral in particular. An Itô integral is a special case of stochastic integrals where a process is integrated with respect to a Brownian motion. In general, the analytical expression of a stochastic integral does not coincide with the expression suggested by Riemann–Stieltjes integrals because the paths of a Brownian motion are not differentiable. This gap is illustrated numerically on a simple example, comparing the tentative explicit solution with the numerical estimation found using the discrete sum approximation. We conclude the chapter by providing the main properties of the Itô integral.

Nurses work in a wide variety of settings, and this includes a wide variety of communities. In Australia and Aotearoa New Zealand, many of these communities are rural and require nurses to have a broad general range of skills to meet the diversity of needs that their clients present with. Rural health nurses may be sole practitioners, providing health care on their own, or as part of a small team that sometimes may include doctors. An increased scope of practice and greater reliance on collaboration, interdisciplinary and transdisciplinary practice is common.

Nurse practitioners (NPs) are a valued addition to the primary health care (PHC) team and are well-placed to increase accessibility to quality health care services while offering consumer choice. NPs have undertaken advanced education and clinical training. In addition, they have demonstrated their competency, capacity and capability to provide high-quality, effective and efficient clinically focused health care delivery. Although many NPs practice in rural or underserviced communities, NPs practice across a diverse range of health care settings, delivering either specialist or generalist health services. Recognised as advanced practice nurses internationally and nationally, the NP role has emerged as a response to meet the challenges of rising health care demand and is proving effective in promoting transformational changes within the PHC sector.

We introduce derivative securities and ask ourselves how to determine their price from a financial perspective. We discover that the cashflow of zero-coupon bonds and forward contracts can be artificially replicated by adopting a static trading strategy featuring primary assets. With almost no math, we obtain the central result that every product whose payoff is a linear function of the future price of tradeable products can be computed without relying on any model. The story is different for products whose payoff is a non-linear function of the future price of assets, such as European calls and puts. In such cases, pricing by replication may still be possible, but is more complex but it requires a model and features a dynamic replicating strategy, evolving through time. We use the law of one price to give a clear interpretation to the no-arbitrage price of derivatives. We conclude the chapter with the general expression of a derivative’s price, given by the risk-neutral expectation of its payoff discounted at the risk-free rate. The purpose of the book is to introduce all the concepts needed to understand why and when this result holds, and how it can be evaluated in practice.

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).