These are all very practical decisions, and the methods of analyzing them make use of Principle 1:A dollar today is not worth the same as a dollar tomorrow. Economists have considered the management of personal financial resources over a lifetime to be a central issue worthy of serious study, and several Nobel Prizes in economics have been awarded for contributions in this area. And, as Box 3.1 shows, financial literacy for a nation’s people is a goal being pursued by countries all over the world.

Most financial decisions boil down to figuring out how much an asset is worth. For example, in deciding whether to invest in a security such as a stock or a bond or in a business opportunity, you have to determine whether the price being asked is high or low relative to other investment opportunities available to you. In addition to investment decisions, there are many other situations in which one needs to determine the value of an asset. For example, suppose that the tax assessor in your town has assessed your house at $500,000 for property tax purposes. Is this value too high or too low? Or suppose you and your siblings inherit some property, and you decide to sell it and share the proceeds equally among yourselves. How do you decide how much it is worth?

In the previous chapters we introduced the concept of valuation, which involved converting cash flows that are expected to happen in the future into today’s terms, and we learned about the returns on various assets and how to analyze the past performance of financial instruments to inform investment decisions. However, the future is not known for sure. The cash flows that occur may be different from what we initially expect, and the value (and rates of return) of financial instruments change over time. In this chapter, we introduce a fundamental concept in finance: Uncertainty about the future can affect valuation and decision making.

We begin by defining what risk is in finance, and how it affects financial decisions. We then dive into how risk can be managed, which includes identifying relevant risks, assessing how they can affect one’s financial situation, and then determining appropriate techniques that can be used to reduce these risks.

Before proceeding with our first steps in valuation, we need to introduce some tools and define some notation that will be used here and throughout the book when valuing assets.

At a fundamental level, the value of an asset comes from the cash flows that are associated with it—that is, from the amounts of money that the owner either receives or pays at various points in time. An essential tool in analyzing cash flows from any financial decision is a diagram known as a timeline, a linear representation of cash outflows and inflows over a period of time. A negative sign in front of a cash flow means that you are paying that amount of money (it’s a cash outflow from you). No sign means that you are receiving an amount of money (it’s a cash inflow to you).

This chapter discusses some of the current trends and promising future directions in the field of cognitive neuroscience of aging. The chapter first discusses recent research investigating the contribution of individual difference factors related to identify, including race, culture, and sex differences. Next, the chapter reviews recent research on neuromodulation, including ways in which noninvasive brain stimulation (e.g., repetitive transcranial magnetic stimulation [rTMS], transcranial direct current stimulation [tDCS], and transcranial alternating current stimulation [tACS]) has been used in an attempt to enhance cognition with age as well as with age-related disorders. This section also considers other approaches to neuromodulation, including deep-brain stimulation and neurofeedback. Finally, discussion of emerging directions considers the importance of investigating aging across the lifespan, studying the intersection of physical health with cognition, exploring the distinction of socioemotional and cognitive domains, and emphasizing the contribution of context with age.