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 Girsanov's 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. Girsanov's 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.

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.

Approximately one in every six people have some form of disability and about one-third of these people have a severe or profound limitation to their daily activities and function. As a subgroup, they are some of the most marginalised and disadvantaged, often experiencing disparate chronic and complex health problems when compared to the general population. In addition, they sometimes encounter disabling challenges accessing the health system and have experienced poor quality care from health professionals whose capacity to understand their needs, and how to best respond to them, is limited. This chapter seeks to inform health care professionals about the intersection of health and disability so that they can better work with people with a disability no matter the health context.

The terms ‘health promotion’ and ‘health education’ are often used interchangeably. Often this is a problem as they are distinct and different concepts. Whitehead attempted to overcome this problem by separating and defining the terms. When it comes to primary health care program planning and evaluation, the terms health promotion and health education are also often used interchangeably but this is less of a problem in this specific case than already stated. Health promotion approaches, often by default, include health education interventions. Reflecting this, many ‘health’ planning and evaluation tools and models incorporate health promotion and health education processes.

A dynamic system is typically described via a differential equation. This is an equation specifying the initial state of the system and the way it evolves through time. The solution to a differential equation is a function, which can always be written as an integral. Sometimes, the latter can be computed explicitly; this analytical expression is known as the explicit solution of the equation. In the presence of uncertainty, the dynamics of the system features stochastic processes, leading to a stochastic differential equation, the solution of which is no longer a deterministic function but is instead a stochastic integral. This is illustrated on a simple example modeling the evolution of the size of a population. Being a stochastic integral, the solution to a stochastic differential equation can be estimated numerically using the so-called Euler scheme, as explained in Chapter 13. This procedure is illustrated on the population size example. Finally, we study how the solution of a differential equation driven by a Brownian motion changes when switching from one probability measure to another thanks to Girsanov's theorem.

Survey studies offer a balance between large-sample analysis and more sample-specific studies, since they can be based on a large sample of cross-sectional companies but at the same time they allow us to ask specific qualitative questions of the respondents. Survey studies also allow us to measure and quantify decision-making processes and beliefs. Thus, survey data analysis can be seen as a bridge connecting qualitative studies to quantitative studies in corporate finance research. This chapter covers the most commonly used techniques in survey data analysis. In particular, it focuses on the assumptions and applications of principal components analysis (PCA), but also briefly explains factor analysis. The chapter also briefly discusses the similarities and differences between these two methods. The chapter includes an example of an application of PCA to ownership concentration by examining the different dimensions of ownership concentration. Finally, lab work on PCA and a mini case study are provided.

We study in detail the replication strategy of derivatives in continuous time. Under the assumptions of the Black–Scholes–Merton model, the delta-hedging strategy performs perfectly on every single trajectory for the stock price. In practice, some assumptions are not met, explaining why perfect replication is essentially theoretical. Replication is important not only to find the no-arbitrage price of a derivative, but also to enable traders to hedge the risks associated with their financial positions. The decision to fully, partially, or not hedge at all depends on the risk appetite of the trading desk, but also on regulatory constraints imposed to the bank. The greeks represent the sensitivities of the derivatives price with respect to some variables or parameters. They allow traders to identify the main risk factors impacting their trading book, hence, suggest how to hedge their positions and explain where the profit and loss (PnL) movements come from. In fact, greeks are to traders and risk managers what control screens are to pilots: they are the indicators allowing them to navigate through the turmoil of financial markets.

This chapter introduces First Nations approaches to health care that have relevance for the Australian and Aotearoa New Zealand contexts. It examines the historical influences that impacted the health and well-being of First Nations in these countries and considers the need for adopting First Nations approaches to health care practice such as cultural safety, cultural responsiveness and other cultural frameworks. Several of the principles for practice are transferrable to international First Nations communities as well as culturally and linguistically diverse populations.

Being given partial information about the outcome of an experiment forces us to revise the probabilities that we assign to events. We show that combining a reference probability space with revealed information suggests replacing the reference probability measure by another, called conditional measure. Consequently, the distributions of random variables also change to conditional distributions in presence of information, in general. The expectation of a random variable conditional upon an event coincides with the standard expectation of the variable provided that the reference probability measure is replaced by the conditional one; that is, provided that one uses the conditional distribution of the random variable instead. Next, we introduce the concept of conditional expectation with respect to a sigma-field. This is the random variable returning the best guess of the random variable given the provided information. We give the explicit form of the Radon–Nikodym derivative connecting the conditional measure to the reference one. We conclude the chapter by computing explicitly some conditional distributions of random variables and with an application to stock price models.

Panel data consist of multiple observations for each unit in the data. The units can be investors, firms, households, and so on. Panel datasets that allow us to follow these units over time provide intuitive understanding of the unit’s behavior. The panel-data analysis tends to be better at addressing the causality issues in research than cross-sectional data. This chapter provides a wide range of examples of panel-data techniques, with the main focus on linear panel-data models. It covers pooled OLS estimators, the fixed-effects model, least-squares dummy variable estimator, difference-in-differences model, between estimator, random-effects model, Hausman–Taylor random-effects IV method, and briefly the dynamic panel-data models. The chapter also reviews stationarity and the generalized method of moments (GMM) briefly. An application of linear panel-data models, as well as lab work and a mini case study, are provided at the end of the chapter.