Finance refers to monetary resources and to the study and discipline of money,currency,assets and liabilities. As a subject of study,it is related to but distinct from economics,which is the study of the production,distribution,and consumption of goods and services. Based on the scope of financial activities in financial systems,the discipline can be divided into personal,corporate,and public finance.
Financial economics is the branch of economics characterized by a "concentration on monetary activities",in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables,such as share prices,interest rates and exchange rates,as opposed to those concerning the real economy. It has two main areas of focus:asset pricing and corporate finance;the first being the perspective of providers of capital,i.e. investors,and the second of users of capital. It thus provides the theoretical underpinning for much of finance.
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless,the most commonly used types of market risk are:
Financial modeling is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business,project,or any other investment.
In statistics,stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities,such as options. The name derives from the models' treatment of the underlying security's volatility as a random process,governed by state variables such as the price level of the underlying security,the tendency of volatility to revert to some long-run mean value,and the variance of the volatility process itself,among others.
The following outline is provided as an overview of and topical guide to finance:
In finance,the Heston model,named after Steven L. Heston,is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model:such a model assumes that the volatility of the asset is not constant,nor even deterministic,but follows a random process.
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial time series typically assume homoskedasticity and normality and as such cannot explain stylized phenomena such as skewness,heavy tails,and volatility clustering of the empirical asset returns in finance. In 1963,Benoit Mandelbrot first used the stable distribution to model the empirical distributions which have the skewness and heavy-tail property. Since -stable distributions have infinite -th moments for all ,the tempered stable processes have been proposed for overcoming this limitation of the stable distribution.
In finance,model risk is the risk of loss resulting from using insufficiently accurate models to make decisions,originally and frequently in the context of valuing financial securities.
Damiano Brigo is a mathematician known for research in mathematical finance,filtering theory,stochastic analysis with differential geometry,probability theory and statistics,authoring more than 130 research publications and three monographs. From 2012 he serves as full professor with a chair in mathematical finance at the Department of Mathematics of Imperial College London,where he headed the Mathematical Finance group in 2012–2019. He is also a well known quantitative finance researcher,manager and advisor in the industry. His research has been cited and published also in mainstream industry publications,including Risk Magazine,where he has been the most cited author in the twenty years 1998–2017. He is often requested as a plenary or invited speaker both at academic and industry international events. Brigo's research has also been used in court as support for legal proceedings.
In the theory of stochastic processes,a part of the mathematical theory of probability,the variance gamma (VG) process,also known as Laplace motion,is a Lévy process determined by a random time change. The process has finite moments,distinguishing it from many Lévy processes. There is no diffusion component in the VG process and it is thus a pure jump process. The increments are independent and follow a variance-gamma distribution,which is a generalization of the Laplace distribution.
Portfolio optimization is the process of selecting an optimal portfolio,out of a set of considered portfolios,according to some objective. The objective typically maximizes factors such as expected return,and minimizes costs like financial risk,resulting in a multi-objective optimization problem. Factors being considered may range from tangible to intangible.
Nicole El Karoui is a French mathematician and pioneer in the development of mathematical finance,born 29 May 1944 in Paris. She is considered one of the pioneers on the French school of mathematical finance and trained many engineers and scientists in this field. She is Professor Emeritus of Applied Mathematics at Sorbonne University,and held professorship positions at the École Polytechnique and Universitédu Maine. Her research has contributed to the application of probability and stochastic differential equations to modeling and risk management in financial markets.
Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing,risk management,investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries. The process usually consists of searching vast databases for patterns,such as correlations among liquid assets or price-movement patterns.
Mathematical finance,also known as quantitative finance and financial mathematics,is a field of applied mathematics,concerned with mathematical modeling in the financial field.
Hélyette Geman is a French academic in mathematical finance. In 2022 she became the first woman in 41 years to be named ‘Financial Engineer of the Year’by the International Association of Financial Engineers. Her career has spanned several sub-disciplines including catastrophic insurance,probability theory,and the finance of commodities. Her academic institutions include ESSEC Business School,the University Paris Dauphine,and Birkbeck,University of London. She is currently a Research Professor at Johns Hopkins University.
In financial mathematics,the Carr–Madan formula of Peter Carr and Dilip B. Madan shows that the analytical solution of the European option price can be obtained once the explicit form of the characteristic function of ,where is the price of the underlying asset at time ,is available. This analytical solution is in the form of the Fourier transform,which then allows for the fast Fourier transform to be employed to numerically compute option values and Greeks in an efficient manner.
An additive process,in probability theory,is a cadlag,continuous in probability stochastic process with independent increments. An additive process is the generalization of a Lévy process. An example of an additive process that is not a Lévy process is a Brownian motion with a time-dependent drift. The additive process was introduced by Paul Lévy in 1937.
Damir Filipović is a Swiss mathematician specializing in quantitative finance. He holds the Swissquote Chair in Quantitative Finance and is the director of the Swiss Finance Institute at EPFL.
In mathematics,the Chan–Karolyi–Longstaff–Sanders process is a stochastic process with applications to finance. In particular it has been used to model the term structure of interest rates. The CKLS process can also be viewed as a generalization of the Ornstein–Uhlenbeck process. It is named after K. C. Chan,G. Andrew Karolyi,Francis A. Longstaff,and Anthony B. Sanders,with their paper published in 1992.
