Financial crisisA financial crisis is any of a broad variety of situations in which some financial assets suddenly lose a large part of their nominal value. In the 19th and early 20th centuries, many financial crises were associated with banking panics, and many recessions coincided with these panics. Other situations that are often called financial crises include stock market crashes and the bursting of other financial bubbles, currency crises, and sovereign defaults.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Subprime mortgage crisisThe United States subprime mortgage crisis was a multinational financial crisis that occurred between 2007 and 2010 that contributed to the 2007–2008 global financial crisis. The crisis led to a severe economic recession, with millions of people losing their jobs and many businesses going bankrupt. The U.S. government intervened with a series of measures to stabilize the financial system, including the Troubled Asset Relief Program (TARP) and the American Recovery and Reinvestment Act (ARRA).
2007–2008 financial crisisThe 2007–2008 financial crisis, or Global Financial Crisis (GFC), was a severe worldwide economic crisis that occurred in the early 21st century. It was the most serious financial crisis since the Great Depression (1929). Predatory lending targeting low-income homebuyers, excessive risk-taking by global financial institutions, and the bursting of the United States housing bubble culminated in a "perfect storm". Mortgage-backed securities (MBS) tied to American real estate, as well as a vast web of derivatives linked to those MBS, collapsed in value.
Great RecessionThe Great Recession was a period of marked general decline observed in national economies globally, i.e. a recession, that occurred from late 2007 to 2009. The scale and timing of the recession varied from country to country (see map). At the time, the International Monetary Fund (IMF) concluded that it was the most severe economic and financial meltdown since the Great Depression. One result was a serious disruption of normal international relations.
Risk premiumA risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. Where is the risky expected rate of return and is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections.
Economic systemAn economic system, or economic order, is a system of production, resource allocation and distribution of goods and services within a society. It includes the combination of the various institutions, agencies, entities, decision-making processes, and patterns of consumption that comprise the economic structure of a given community. An economic system is a type of social system. The mode of production is a related concept.
Deep reinforcement learningDeep reinforcement learning (deep RL) is a subfield of machine learning that combines reinforcement learning (RL) and deep learning. RL considers the problem of a computational agent learning to make decisions by trial and error. Deep RL incorporates deep learning into the solution, allowing agents to make decisions from unstructured input data without manual engineering of the state space. Deep RL algorithms are able to take in very large inputs (e.g.
Hyperbolic partial differential equationIn mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
