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.
In mathematical finance, a risk-neutral measure is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free.
The fundamental theorems of asset pricing, in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitrage-free, and for a market to be complete. An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss. Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit. The first theorem is important in that it ensures a fundamental property of market models. Completeness is a common property of market models. A complete market is one in which every contingent claim can be replicated. Though this property is common in models, it is not always considered desirable or realistic.
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.
In financial economics, asset pricing refers to a formal treatment and development of two interrelated pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance.
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.
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator. In recent years attention has turned towards convex and coherent risk measurement.
In financial mathematics, acceptance set is a set of acceptable future net worth which is acceptable to the regulator. It is related to risk measures.
A consistent pricing process (CPP) is any representation of (frictionless) "prices" of assets in a market. It is a stochastic process in a filtered probability space such that at time the component can be thought of as a price for the asset.
No free lunch with vanishing risk (NFLVR) is a concept used in mathematical finance as a strengthening of the no-arbitrage condition. In continuous time finance the existence of an equivalent martingale measure (EMM) is no more equivalent to the no-arbitrage-condition, but is instead equivalent to the NFLVR-condition. This is known as the first fundamental theorem of asset pricing.
In mathematics and information theory of probability, a sigma-martingale is a semimartingale with an integral representation. Sigma-martingales were introduced by C.S. Chou and M. Emery in 1977 and 1978. In financial mathematics, sigma-martingales appear in the fundamental theorem of asset pricing as an equivalent condition to no free lunch with vanishing risk.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In finance, an admissible trading strategy or admissible strategy is any trading strategy with wealth almost surely bounded from below. In particular, an admissible trading strategy precludes unhedged short sales of any unbounded assets. A typical example of a trading strategy which is not admissible is the doubling strategy.
David Clay Heath was an American probabilist known for co-inventing the Heath–Jarrow–Morton framework to model the evolution of the interest rate curve.
Elyès Jouini is a French Tunisian economist and Distinguished Professor of Economics at the University of Paris Dauphine. His research is mainly in the area of financial economics, in particular transaction costs, heterogeneous beliefs, aggregation, long-term risk and the maturity structure of interest rates. After early research on general equilibrium theory, he got interested in modeling financial markets by including both economic and financial dimensions as well as dimensions pertaining to psychology or sociology. His research has been acknowledged by the Best Young French Economist Award in 2005 (together with Esther Duflo, 2008's Best Paper Award in Finance by Europlace Institute of Finance, and the 2009 Finance and Sustainability European Research Award, and was named Chevalier de la Legion d'honneur in 2010.
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 probability theory, Yan's theorem is a separation and existence result. It is of particular interest in financial mathematics where one uses it to prove the Kreps-Yan theorem.
In probability theory, Kramkov's optional decomposition theorem is a mathematical theorem on the decomposition of a positive supermartingale with respect to a family of equivalent martingale measures into the form
