This chapter provides an introduction to the book. The book aims to deepen the reader’s (Bachelor and higher) understanding of empirical research in corporate finance studies and improve their ability to apply econometric methods in their own studies. It may not be general enough for an econometrics course for all finance students, including those interested in asset-pricing studies. However, some of the examples in the book cover studies of the behavior of individual/institutional investors and how this relates to the cost of capital of firms. This link is important to understand in empirical corporate finance studies. The chapter provides a short discussion on this link and then provides a detailed outline of the book. The book is a practical method book, covering essential basic econometric models to illustrate how to apply them in research, closely following some of the well-written and pedagogical books in econometrics.

Chronic conditions, or non-communicable diseases, are the leading cause of death worldwide. Chronic conditions are responsible for 41 million deaths and 17 million premature deaths across the world each year. Most of these deaths are due to four major conditions: cardiovascular disease, cancer, chronic respiratory disease and diabetes. However, other chronic conditions, including injuries that result in persistent disability and mental health disorders, also contribute to increased morbidity and mortality. The significant increase in preventable chronic conditions and the need to manage these are major healthcare concerns of the industrialised world.

Chapter 14 highlights that the solution to a stochastic differential equation cannot be found by treating the sample paths of stochastic processes as smooth functions of time. This is because of the nonzero quadratic variation of a Brownian motion. The purpose of Ito’s lemma is to account for this phenomenon and provides the expression of the differential of a function of a Brownian motion. This is explained using a Taylor expansion and is generalized along various dimensions. The martingale representation theorem highlights that, in some circumstances, any non-negative martingale takes the form of an exponential martingale. Therefore, in such a framework, Girsanov’s theorem does not only work for `special’ measure changes (where the Radon–Nikodym derivative process (RNDP) would coincide with an exponential martingale), but actually encompasses every equivalent measure. We establish a formal link between driftless differential equations and the martingale property of its solution. The RNDP process leading to the risk-neutral measure seen in Chapter 11 is the exponential martingale whose coefficient is such that the drift of the stock price becomes equal to the risk-free rate.

Primary health care (PHC) is a philosophy or approach to health care where health is acknowledged as a fundamental right, as well as an individual and collective responsibility. A PHC approach to health and health care engages multisectoral policy and action which aims to address the broader determinants of health; the empowerment of individuals, families and communities in health decision making; and meeting people’s essential health needs throughout their life course. A key goal of PHC is universal health coverage, which means that all people have access to the full range of quality health services that they need, when and where they need them, without financial hardship.

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.

In the ‘classic’ sense, health professionals often view the health of individuals from a three-part biopsychosocial model of health. In this case, the ‘psych’ part relates directly to ‘mental health’. However, it is important to resist the temptation to separate this part from the bio and social aspects of the well-established model. Instead, it is best to view all parts of the established model as equally important and inter-related to each other. For instance, it is difficult to maintain good mental health and well-being if we lack either good social or ‘bio’ (physical) health. Traditionally, however, health professionals have tended to focus on the physical health component of the biopsychosocial model, especially those working in acute hospital/clinic environments. From a primary health care perspective, the ‘social’ (community development-focused) aspect is supposed to be the most dominant part of the model.

This chapter revisits the concepts of random variable, sigma-field, and measurability in a dynamic fashion. A stochastic process is a time-indexed sequence of random variables used to model a quantity that evolves through time. Similarly, filtration and adaptivity are the natural dynamic extensions of sigma-field and measurability. The sample path of a stochastic process is its trajectory associated with a specific outcome. A martingale is a stochastic process whose current value is also the best guess of its value at any future point in time. We show that increments of martingales are uncorrelated over independent periods and that the conditional expectation of a random variable given the available information is a martingale. In the special case where this random variable is a Radon–Nikodym derivative, its expectation conditional upon the information available at time t is a non-negative martingale with unit expectation called the Radon–Nikodym derivative processes. This allows us to revisit the change-of-measure formula for the expectation of a random variable given the information at time t. We conclude the chapter with the concept of quadratic variation and various examples.

The Monte Carlo method is a powerful approach providing a numerical estimate of an integral using random samples drawn from a given distribution and is perhaps the most widely used numerical method to estimate the price of complex derivative securities. This is because any integral can be written as an expectation of a function of a random variable following a given distribution, and this expectation can be estimated by averaging independent samples drawn from the corresponding distribution, as per the law of large numbers. This suggests that any integral, but also any expectation or probability, can be estimated arbitrarily well by averaging a sufficiently large number of random samples. Most computational software includes random number generators, drawing samples from the uniform distribution. Samples from other distributions can be easily obtained by transforming those uniform samples according to the probability integral transform seen in Chapter 2. The last section briefly introduces control variate and importance sampling, which are two improvements to the plain Monte Carlo method aiming to provide better estimates at fixed computational cost.

Sexual health nurses are employed to work in a range of practice settings and work with diverse population groups. Sexual and reproductive health care is considered a human right and is fundamental to positive well-being. The nurses role in sexual and reproductive health varies between settings within and across different jurisdictons. Work settings include dedicated sexual health clinics, family planning services, community health centres, women’s health services, correctional services, general practices and tertiary education settings. In some juristictions, nurses also provide care in publicly funded sexual health clinics aimed at providing services to specific priority population groups to increase their access to services and reduce the prevalence of adverse sexual and reproductive health outcomes including sexually transmitted infections and unplanned pregnancy.

Previous chapters aimed to present different research designs and econometric models used in empirical corporate finance studies. In this chapter, the focus is on the structure and writing of your research findings. Good writing is key to conveying the findings from your research to readers. You should be able to demonstrate your critical and analytical skills, and discuss the results from your research in a structured way when writing your thesis or academic paper. This chapter discusses the details of the sections included in empirical papers, and thus presents a standard example of the structure of an empirical corporate finance paper. This structure is general and may differ depending on the type of empirical paper and the field. However, beginning with the standard content of the sections will help you to better structure your ideas and writing. The chapter ends by providing some writing suggestions.

Home-based care is common practice in many countries and has had a long tradition in Australia and Aotearoa New Zealand. Home-based care now takes many forms, including the acute care program Hospital in the Home, a range of chronic disease programs and community aged care. Home-based care provides many benefits to consumers, reducing their need to travel to services and associated costs. It also allows the health care provider to have a holistic picture of the consumers and for the consumers to feel empowered to manage their health care issues in their own homes, while continuing with normal daily activities in a setting that they are comfortable in.

In some circumstances, the no-arbitrage price of a product is given by the risk-neutral expectation of the payoff discounted at the risk-free rate. However, we have seen in Chapters 3, 4, and 7 that the conditional expectation of a variable computed under a given measure coincides with the expectation under another measure provided that, in the latter, we rescale the variable with the Radon–Nikodym derivative process (RNDP) connecting the two measures. Applying this to our pricing application shows that, in fact, one is free to choose the measure under which the price will be computed, provided that the discounted payoff is adjusted for the prevailing RNDP connecting the risk-neutral and the chosen measures. This RNDP takes the form of the ratio of two price processes called numéraires. This procedure is called change-of-numéraire and allows to find the price of products in more sophisticated models or of more sophisticated products in the Black–Scholes–Merton setup. The cases of European call with stochastic risk-free rate and of exchange (Margrabe) options are developed in detail.

Brownian motion is a continuous-time process obtained by taking the limit of a scaled random walk. Alternatively, a Brownian motion can be defined in an axiomatic way, using a set of fundamental properties including the normal distribution feature. We consider various transforms of the latter, including scaling, shifting, and the exponential transform. The latter gives rise to the geometric Brownian motion, which is often used to model asset prices or to build Radon–Nikodym derivatives processes. We conclude the chapter by proving Girsanovs theorem. We recall that the distributions of random variables depend on the probability measure at hand, hence, the distributional properties of a stochastic process are impacted by a change of measure. Consequently, a process may display different properties (e.g., different distributions) under different measures. In particular, a process may display the properties of Brownian motions under one measure, but not under another measure. Girsanovs theorem explains how Brownian motion properties are impacted when changing the probability measure using an exponential martingale as the Radon–Nikodym derivative process.

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.