bluuebunny/crossref_metadata_2025_split huggingface dataset:
S
amuelson,
P
aul
A
.
Authors: Merton Robert C. 
Published: May 2010

Abstract

Paul Samuelson's research contributions to quantitative finance have been foundational and wide‐ranging. He was a pioneer in recognizing the importance of option and warrant pricing to finance. His 1965 pricing model introduced geometric Brownian as the prototypical underlying stock price process, developed the partial differential equations for pricing that later produced the Black–Scholes formula, formulated and analyzed the pricing of options that permit early exercise, and introduced the binomial model approximation for geometric Brownian motion. Samuelson was the first to derive the martingale property of properly anticipated speculative price changes in formulating what has come to be known as the
efficient market hypothesis
. Some of his other contributions include reconciling the axioms of expected utility theory with the Markowitz–Tobin mean–variance criterion of choice, exploring the foundations of diversification and optimal portfolio selection with fat‐tailed, infinite‐variance return distributions, and using dynamic portfolio‐selection models to study the systematic dependence on age of optimal portfolio strategies, in particular, optimal long‐horizon investment strategies.
Mandelbrot, Benoit
Authors: Cont Rama 
Published: May 2010

Abstract
Benoit Mandelbrot, the founder of fractal geometry, has been, among numerous other contributions to fields ranging from mathematics to hydrology, an early contributor to the then‐nascent field of stochastic modeling in finance. Obsessed with the wild variability of financial market prices, he was the first to advocate the use of heavy‐tailed distributions and power laws, Lévy processes, and long‐range dependence for modeling market fluctuations.
Merton, Robert C.
Authors: Chan Alex Hamilton 
Published: May 2010

Abstract
Robert C. Merton is John and Natty McArthur University Professor at Harvard Business School. He shared the Nobel Prize in Economic Sciences in 1997. He introduced Ito calculus to finance and economics and made significant contributions in asset pricing, corporate finance, empirical finance, and financial systems. His most notable works include the intertemporal capital asset pricing model, the Black–Scholes–Merton option pricing formula, the Merton jump‐diffusion model, and the Merton structural model for credit risk.
Utility Theory: Historical Perspectives
Authors: Žitković Gordan 
Published: May 2010

Abstract
We present a short survey of the history of utility theory. Starting from the seminal idea of Daniel Bernoulli, we proceed to discuss the work of Herman Gossen and its importance for the “Marginalist revolution”. The next milestone is the advent of axiomatic approaches, starting with the work of Franz Alt, John von Neumann, and Oskar Morgenstern. Various critiques of the expected‐utility model are discussed. On the conceptual side, we mention the “Subjectivist revolution” lead by Leonard Savage, and, on the empirical side, we discuss the paradoxes of Maurice Allais and Daniel Ellsberg and their partial resolution in the work by Daniel Kahneman and Amos Tversky. Finally, we touch upon the concept of risk aversion and the place of utility theory in modern finance.
Option Pricing Theory: Historical Perspectives
Authors: Jarrow Robert A. 
Published: May 2010

AbstractThis article traces the history of the option pricing theory from the turn of the twentieth century to the present. This historical perspective is divided into four sections. The first, entitled “the early years”, discusses the development of option pricing theory before the Black–Scholes–Merton model (1973). The second section discusses the Black–Scholes–Merton model and its extensions. The third section discusses the Heath–Jarrow–Morton model for pricing interest rate derivatives. The last section discusses credit risk derivative pricing models.
Modern Portfolio Theory
Authors: French Craig W. 
Published: May 2010

AbstractAlthough the prehistory of modern portfolio theory stretches back all the way to Bernoulli, the more proximate origins lie in the work of Markowitz and others in the 1950s. The discovery of the capital asset pricing model in the 1960s brought this line to intellectual maturity by embedding the portfolio choice problem in a proper asset‐pricing equilibrium framework. Subsequent work has been involved with extensions, refinements, and applications.
Bubbles and Crashes
Authors: Kaizoji Taisei , Sornette Didier 
Published: May 2010

AbstractWe review some of the hypotheses offered to explain the market crashes that often follow asset price bubbles. Starting from historical accounts and syntheses of past bubbles and crashes, we put the problem in perspective with respect to the development of the efficient‐market hypothesis. We then present the models based on heterogeneous agents and the limits to arbitrage that prevent rational agents from bursting bubbles before they inflate. Then, we explore another set of explanations of why rational traders would be led to actually profit from and surf on bubbles, by anticipating the behavior of noise traders or by realizing the difficulties in synchronizing their actions. We end by discussing a complex system approach, in which bubbles are the result of a collective emergent organization of human agents interaction through social imitation and herding. In this framework, the end of a bubble is modeled as a bifurcation (or phase transition), which offers new insights for diagnostic and prognostic. The key insight is that diagnosing bubbles may be feasible when the positive feedback mechanisms that give rise to transient “superexponential” price growth are taken into account.
Fisher, Irving
Authors: Dimand Robert W. 
Published: May 2010

AbstractThe American economist Irving Fisher (1867–1947) of Yale University introduced general equilibrium analysis into North American economics in his 1891 dissertation, and went on to become a leading monetary and capital theorist. The “Fisher equation” of hisAppreciation and Interest(1896) viewed nominal interest as the sum of real interest and expected inflation (which he later modeled as a distributed lag of price changes). The “Fisher diagram” ofThe Rate of Interest(1907) showed optimal consumption and saving in a two‐period model, the basis of all subsequent analyses of intertemporal allocation. Fisher'sThe Purchasing Power of Money(1911) restated the quantity theory of money, with monetary shocks driving output fluctuations in the short run but affecting only nominal variables in the long run. His 1926 paper correlating unemployment and a distributed lag of inflation was reprinted in 1973 as “Lost and Found: I Discovered the Phillips Curve—Irving Fisher.” The “Fisher index”, the geometric mean of the Paasche and Laspeyres indexes, is now widely used as an index number. Emphasizing that inflation makes money and bonds risky, Fisher was an enthusiast for investment in common stocks in the 1920s. He shattered his public reputation with his October 1929 statement that stock prices had reached a permanently high plateau.
Modigliani, Franco
Authors: Szenberg Michael , Ramrattan Lall 
Published: May 2010

AbstractFranco Modigliani, the 1980 Nobel laureate, was a leader in Keynesian economics. He has moved Keynesian theory to the empirical forefront by constructing the first Federal Reserve Board macroeconometric model in the country. Modigliani has further expanded the Keynesian consumption function in the direction of his life cycle hypothesis (LCH), and the Keynesian investment function in the direction of the Modigliani and Miller (M&M) hypothesis, creating a research program for current economic analysis. A particular signature of Modigliani's Keynesian contribution is his specification of the financial sector as the driver of the Federal Reserve Board econometric model, in which he incorporated his lifetime research on liquidity preference.
Arrow, Kenneth
Authors: Chichilnisky Graciela 
Published: May 2010

AbstractThis article summarizes the theory of markets under uncertainty, developed by Arrow and Debreu. It describes the achievements of the theory, the critical issues that it raises, and its large legacy. This article also focuses on the way Arrow introduced securities: how he defined them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow's theory of risk bearing that follows the axiomatic treatment of Von Neumann and Morgenstern, Milnor, Hernstein, De Groot, and Villegas. In terms of Arrow's legacy, it is now known that the classic expected utility theory embraces normal or frequent risks at the expense of neglecting rare events, even those with important consequences such as catastrophes, causing paradoxical experimental behavior. Kenneth Arrow encouraged the creation of a more recent extension of classic axiomatic theory of choice under uncertainty, and, in the early 1990s, we proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and of choices under uncertainty that conform better to the experimental evidence. The introduction of markets with “endogenous uncertainty” in the early 1990s extended and challenged the foundation of the Arrow–Debreu theory of markets by considering risks that are created by the workings of the economy, resulting in the breakdown of the equivalence between markets with and without uncertainty that prevails in the Arrow–Debreu theory. This led to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008–2009. In 1999, Arrow himself contributed to the theory of endogenous uncertainty in his work with Frank Hahn.
Bernoulli, Jacob
Authors: Sylla Edith Dudley 
Published: May 2010

Abstract

In
The Art of Conjecturing
(1713), Jacob Bernoulli aimed at applying the mathematics previously developed in Christiaan Huygens'
On Reckoning in Games of Chance
to civil, moral, and economic matters. Although most of the mathematics in Bernoulli's book derived from commercial arithmetic, algebra, and combinatorics, Jacob Bernoulli's greatest achievement in the book was to prove what was later called the
weak law of large numbers
. On the basis of this law, Bernoulli proposed that the probabilities of events could be discovered,
a posteriori
, from the results many times observed in similar situations.
Rubinstein, Edward Mark
Authors: Namvar Ethan 
Published: May 2010

AbstractMark Rubinstein has been described as a “brilliant scholar,” one who “marches to his own drumbeat,” and is known among colleagues as a risk taker and innovator. As an individual, Rubinstein is often characterized as intellectually fearless. He is known by many of his students as a sincere mentor who has extraordinary passion and intellect.Having developed the binomial options model with Stephen A. Ross and John C. Cox, he revolutionized the way professionals value options. For this and earlier work on asset pricing models, he was elected President of the American Finance Association for 1993. Along with his colleagues Hayne E. Leland and John W. O'Brien, Rubinstein developed and commercialized the use of portfolio insurance, which was ultimately cited as one of the causes of the stock market crash of 1987, and his firm developed the first exchange‐traded fund in 1992. The International Association of Financial Engineers (IAFE) named him as the 1995 IAFE/SunGard Financial Engineer of the Year, making him the third winner after Robert Merton and Fischer Black.
Heavy Tails
Authors: Davis Richard A. 
Published: May 2010

AbstractThe log‐returns of most financial assets exhibit bursts of outlying observations that are characteristic of heavy tails. As such, models formulated for financial time series must capture heavy‐tailedness. Regular variation is a natural and often used concept to describe and model heavy‐tailed phenomena. This article first provides some evidence for heavy tails in log‐returns and then describes the basics of regular variation. It turns out that the two most commonly used models for financial time series, the GARCH and heavy‐tailed stochastic volatility (SV) processes, have finite‐dimensional distributions that are regularly varying. Regular variation is also a powerful tool for deriving large sample properties of important statistics of financial time series, from maxima to sample autocorrelations of functions of the process. These techniques show that although GARCH and SV processes share many common features, there can be a substantial difference in the large sample properties of the maxima and sample autocorrelations.
Skorokhod Embedding
Authors: Obłój Jan 
Published: May 2010

AbstractThe Skorokhod embedding problem, in its essence, amounts to designing a stopping time such that, at that time, a given stochastic process has a prescribed distribution. It has been an active field of research in probability for over 40 years now. We discuss some of the key results in the domain, along with their applications in financial mathematics, namely, in robust pricing and hedging of exotic derivatives. More precisely, we establish a correspondence between solutions to the Skorokhod embedding problem and possible market models matching given prices of vanilla options for a fixed maturity. No‐arbitrage bounds on a price of an exotic derivative are then obtained through an optimization over solutions to the embedding problem. Pathwise understanding of the embedding often allows us to derive the associated robust (often model‐free) superhedges. We illustrate these techniques with an example of a one‐touch option. No‐arbitrage bounds on its price are induced by the Azéma–Yor and Perkins solutions to the Skorokhod embedding; the associated superhedging strategy was deduced by Hobson.
Markov Processes
Authors: Bossy Mireille , Champagnat Nicolas 
Published: May 2010

AbstractWe present the main concepts of the theory of Markov processes: transition semigroups, Feller processes, infinitesimal generator, Kolmogorov's backward and forward equations, and Feller diffusion. We also give several classical examples including stochastic differential equations (SDEs) and backward stochastic differential equations (BSDEs) and describe the links between Markov processes and parabolic partial differential equations (PDEs). In particular, we state the Feynman–Kac formula for linear PDEs and BSDEs, and we give some examples of the correspondence between stochastic control problems and Hamilton–Jacobi–Bellman (HJB) equations and between optimal stopping problems and variational inequalities. Several examples of financial applications are given to illustrate each of these results, including European options, Asian options, and American put options.
LéVy Copulas
Authors: Tankov Peter 
Published: May 2010

AbstractLévy copulas characterize the dependence among components of multidimensional Lévy processes. They are similar to copulas of probability distributions, but are defined at the level of Lévy measures. Lévy copulas separate the dependence structure of a Lévy measure from the one‐dimensional marginal measures, enabling one to construct parametric multidimensional Lévy models by combining arbitrary one‐dimensional Lévy processes with a Lévy copula from a parametric family. In finance, Lévy copulas are useful to model joint moves of several assets in various settings, including portfolio risk management, option pricing, insurance, and operational risk.
Convex Duality
Authors: Scandolo Giacomo 
Published: May 2010

Abstract

In this article, we provide a brief account of convex duality, a set of tools for the analysis of convex optimization problems. The unifying principles underlying these methods can be traced back to the basic duality that exists between a convex set of points in the plane and the set of supporting lines (hyperplanes.) First, we describe, in a finite‐dimensional setting, Lagrange duality, maybe the simplest form of duality. It is usually known as the
Lagrange multiplier method
. Then we introduce Fenchel duality; this is presented as a by‐product of Lagrange duality, even though these two forms of duality are formally equivalent. Finally, we discuss Lagrange and Fenchel duality in an infinite‐dimensional setting.
Arbitrage Pricing Theory
Authors: Reisman Haim 
Published: May 2010

Abstract
The arbitrage pricing theory (APT) explains expected returns of portfolios in a given sequence of assets. The model identifies sets of reference variables with respect to which expected returns of portfolios have a multibeta representation. This is done under the assumption that the assets in the sequence have a factor structure and that there are no portfolios with large expected returns and unit variance. The model predictions may have approximation errors that disappear when the model is applied to diversified portfolios.
Efficient Market Hypothesis
Authors: LeRoy Stephen F. 
Published: May 2010

Abstract
Despite the fact that the topic of capital market efficiency plays a central role in introductory instruction in finance, it is difficult to determine exactly what it means. Fama's well‐known statement that market efficiency can be tested only jointly with an assumed returns model implies that market efficiency generates restrictions on the data that are distinct from those implied by particular models. It is difficult to find a clear characterization of what these additional restrictions are. One possibility is that the proponents of this theory identified market efficiency with rational expectations. Another possibility (suggested by empirical tests of efficiency) is that an efficient market is one in which expected returns are constant. A third possibility is that an efficient market is one in which asset prices are similar to those that would occur in the absence of frictions. All of these interpretations have difficulties. It is concluded that distinguishing market efficiency from particular returns models is a questionable research strategy.
Arbitrage Strategy
Authors: Kardaras Constantinos 
Published: May 2010

Abstract

A (riskless)
arbitrage strategy
allows a financial agent to make certain profit out of nothing, that is, out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium state, as opportunities for riskless profit would result in an instantaneous movement of prices of certain financial instruments. The principle of not allowing for arbitrage opportunities in financial markets has far‐reaching consequences, most notably the option‐pricing and hedging formulas in complete markets.
Fundamental Theorem of Asset Pricing
Authors: Schachermayer Walter 
Published: May 2010

AbstractThe fundamental theorem of asset pricing states that the absence of arbitrage in a market (model) is essentially equivalent to the existence of an equivalent probability measureQunder which the prices of tradable securities have the martingale property. We give a precise formulation of this theorem and discuss the origins and history of this theorem, which is one of the pillars of mathematical finance.
Risk‐Neutral Pricing
Authors: Schachermayer Walter 
Published: May 2010

Abstract
We review the valuation of uncertain future cash flows. This article has a history of several centuries in the actuarial literature as well as in Bachlier's “fundamental principle” for the valuation of options. The technique, which is a basic tool in mathematical finance, consists in calculating the expected value of the discounted cash flows. The crucial point is that we calculate this expectation under a so‐called “risk neutral” probability measure. In the context of the Black–Scholes model, the risk neutral measure is the unique probability measure which is equivalent to the given “physical” or “historic” probability measure and under which the discounted stock price process is a martingale.
Superhedging
Authors: Campi Luciano 
Published: May 2010

Abstract

In incomplete financial markets, the lack of replicability of contingent claims justifies the introduction of superhedging. Given a contingent claim
H
, a superhedging strategy is an admissible strategy that super‐replicates
H
at maturity. The initial endowment that allows to pursue that strategy is called the
superhedging price
. This article is a short survey of the main results on this topic in the mathematical finance literature. We focus especially on continuous‐time hedging of European‐type options.
Free Lunch
Authors: Kardaras Constantinos 
Published: May 2010

Abstract

The concept of
absence of opportunities for free lunches
is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights in quantitative finance. Formulating rigorously, the exact definition of absence of opportunities for riskless profit turned out to be a highly nontrivial fact that troubled mathematicians and economists for at least two decades. The purpose of this article is to give a quick (and, hence necessarily, incomplete) account of the recent work aimed at providing a simple and intuitive no‐free‐lunch assumption that would suffice in formulating a version of the celebrated fundamental theorem of asset pricing.
Minimal Entropy Martingale Measure
Authors: Schweizer Martin 
Published: May 2010

AbstractSuppose that discounted asset prices in a financial market are given by aP‐semimartingaleS. Among all probability measuresQthat turnSinto a localQ‐martingale, the minimal entropy martingale measure is characterized by the property that it minimizes the relative entropy with respect toP.Viaconvex duality, it is intimately linked to the problem of maximizing expected exponential utility from terminal wealth. It also appears as a limit ofp‐optimal martingale measures aspdecreases to 1. Like for most optimal martingale measures, finding its explicit form is easy ifSis an exponential Lévy process and quite difficult otherwise.
Minimal Martingale Measure
Authors: Föllmer Hans , Schweizer Martin 
Published: May 2010

AbstractSuppose discounted asset prices in a financial market are given by aP‐semimartingale of the formS = S0 + M + A. The minimal martingale measure forSis characterized by the properties that it turnsSinto a local martingale and preserves the martingale property for any localP‐martingale stronglyP‐orthogonal toM. It plays a key role in finding locally risk‐minimizing strategies, and it comes up in various other contexts as well. Importantly, its density process can be written explicitly in terms ofMandA, so that one can use it very generally and broadly. In some specific settings, it also has other optimality properties.
Good‐Deal Bounds
Authors: Hodges Stewart D. 
Published: May 2010

Abstract
Good‐deal bounds provide a range of prices within which an instrument must trade if it is not to offer a surprisingly good reward‐for‐risk opportunity. This approach to valuation provides an important middle course between finding a unique value and finding probably weak bounds based on super‐replication. In a world where derivatives are difficult to hedge precisely, good‐deal bounds reflect this; they depend on model assumptions and on the prices of the securities that would be used to exploit mispricing.
Good‐deal bounds have two interpretations: we can think of them either as establishing normative bid and ask forward prices for a particular trader, or as predicting a range in which we expect the market price to lie.
We cover the main issues without going too deeply into mathematical technicalities, describing the nature of the construction and giving insights into the analysis, including the use of duality in the solutions. We also sketch the history of the topic, including that of the closely related generalized Sharpe ratio, and the link to coherent risk measures. There is also a discussion of the role of the utility function. The article concludes with a short account of the more recent and prospective literature.