Financial economics is a field in which people have been continuously using economic theory to explore and study equilibrium and arbitrage, single-period risk allocation and multi-period risk allocation, and optimal investment in finance since the late 1980s. Portfolio, mean variance analysis, optimal consumption and investment, security valuation and pricing, etc., gradually formed and developed a new interdisciplinary discipline of economics and finance. Today, the role of financial economics in the education and training of economists is even more important than in previous years. Such changes often result from corresponding shifts in financial markets in recent years. In financial markets, trillions of dollars' worth of assets are traded daily in derivative securities, such as options and futures, which have been around for decades. However, the importance of these changes is less obvious than the changes themselves. To the extent that derivative securities can be valued by arbitrage, such securities exactly replicate the underlying security. For example, given that the assumptions underlying the Black-Scholes-Merton model (Black, Scholes, and Merton) of option pricing are all correct, the entire options market is redundant because we know from the assumptions , option returns can be replicated using stocks and bonds. The same discussion can be applied to other derivatives securities markets. Therefore, it can be shown that the variable that plays an important role - consumption allocation - is not affected by changes in financial markets. Along these lines, one does not infer the importance of financial markets from their trading volumes, as one would infer the importance of financial markets from similar discussions of supermarket clerks or bank tellers based on their handling of large amounts of cash.

A seemingly more reasonable explanation for the expanding role of financial economics is based on the rapid development in this field. Some 25 years ago, financial theory was little more than a combination of customary descriptions and empirical practices created by practitioners that had little basis in analysis and, for that matter, the results were rarely correct. Financial economists believe that security prices should, in principle, be analyzable using rigorous economic theory. However, in fact, most economists have not devoted more efforts to develop economics in this direction. Today, by contrast, financial economics continues to occupy a central position in economic analysis that involves both time and uncertainty issues. Previously, this was the province of monetary economics; finance methods are increasingly used to analyze problems beyond those involving security prices and portfolio choices, especially when these involve both time and uncertainty. One example is the study of real options, where financial tools originally developed from the analysis of options have been applied to fields such as environmental economics. This field does not deal with options per se, but the issues involved are very closely related to options thinking. Financial economics lies at the intersection of finance and economics. The two disciplines are ideologically different, and rather than stating the differences, people point out their substantial similarities. Finance departments exist within business schools and are oriented toward financial practitioners; whereas economics departments exist within college or university liberal arts departments and are not oriented toward any single non-academic group. From the perspective of an economist who studies finance, the most important difference is that financiers typically use continuous-time models, while economists use discrete-time models. People find that continuous-time finance is more difficult to process and research mathematically than discrete-time finance, and then people ask why financial scientists love continuous-time finance. This issue is rarely discussed. Differences in products do partly explain this, but the role of barriers to entry must also be taken into account. However, the reason why financial scientists prefer to use continuous-time models is because the problems in finance are very different from those in economics. For example, in finance, we need to study the valuation of derivative securities, which can be more accurate using continuous-time models. Handle it well. The technical reasons are related to risk aversion factors in financial market models regarding equilibrium security prices. In many settings, risk aversion is best handled by some transformation of the probability measure of valuation returns. Under very weak assumptions, transformations in continuous time will affect the drifts of the stochastic processes that characterize the evolution of security prices, but will not affect their volatility (according to Girsanov's theorem). This is confirmed in the derivation of the Black-Scholes option pricing formula.

In contrast, it is easy to demonstrate using examples that transformations of the underlying measure in a discrete-time model affect volatility and drift. In addition, it is known that the more factors that do not appear in continuous time, the more likely they are to appear in discrete time as a second-order term of the length of the time interval. The presence of these higher-order terms often makes the discrete-time form of the valuation problem intractable. In a continuous time context, basic analysis is easy to perform, even to the point where one must eventually discretize the resulting partial differential equations in order to obtain numerical solutions. Despite this, most financial economics methods textbooks published in recent years generally start with discrete time and discrete state models when entering the course. It is usually assumed that there is a time interval, that is, some basic concepts and models are introduced on a single-period framework. This setting is more suitable for research on the relationship between security risks and returns, as well as the role of securities in risk allocation.

Then, transition to content under multi-period (limited multiple periods) and continuous time conditions. Multi-period models allow for an asymptotic solution to uncertainty and make it possible to treat important trading securities as new information.