bluuebunny/crossref_metadata_2025_split huggingface dataset:
Kelly Problem
Authors: MacLean Leonard C. , Ziemba William T. 
Published: May 2010

Abstract
The Kelly investment strategy, namely, the period‐by‐period maximization of the expected value of a logarithmic utility function of final wealth has many good properties and some poor ones. It maximizes final wealth asymptotically and minimizes the time to achieve asymptotically large goals. But in the long run, it is very risky because its Arrow–Pratt risk aversion is essentially zero. It is the riskiest utility function one should ever use. Negative power utility, for lognormally distributed assets, is equivalent to fractional Kelly strtegies that blend cash with Kelly optimal weighting. These strategies provide a smoother wealth path but usually end up with less final wealth. Hence there is a growth–security trade‐off.
Merton Problem
Authors: Bergman Yaacov Z. 
Published: May 2010

AbstractThe Merton problem is casting the classical consumer theory in a continuous time framework. Given an initial wealth and a set of capital assets whose prices follow correlated Ito processes, the consumer selects a lifetime consumption program that he most prefers. He selects the program that is optimal for him out of all feasible consumption programs that he can achieve by investing his available wealth continuously in a dynamically managed portfolio of the available capital assets. When the consumer's preference over consumption programs is represented by an additive (or even recursive) utility functional, then his optimization problem can be solved by dynamic programming. This problem and its solution are described in this entry.
Mean–Variance Hedging
Authors: Schweizer Martin 
Published: May 2010

AbstractSuppose discounted asset prices in a financial market are given by aP‐semimartingaleS. Mean–variance hedging is the problem of approximating, with minimal mean‐squared error, a given payoff by the final value of a self‐financing trading strategy. Mean–variance portfolio selection consists of finding a self‐financing strategy whose final value has maximal mean and minimal variance. In both cases, this leads to projecting a random variable inL2(P) onto a space of stochastic integrals ofS, and, apart from proving closedness of that space, the main difficulty is to find more explicit descriptions of the optimal integrand. Both problems have a wide range of applications, and many examples and solution techniques can be found in the literature. Nevertheless, challenging open questions still remain.
Value‐at‐Risk
Authors: Dowd Kevin 
Published: May 2010

Abstract
This article provides a brief overview of Value at Risk (VaR). It defines the VaR and explains the parameters on which it is predicated. It explains the uses to which the VaR has been put, including its uses to determine risk targets and position limits, allocate capital, guide investment, trading and hedging decisions, remunerate traders managers, and disclose risks. It then discusses the attractions of the VaR: it is defined in terms of an easily understood metric (namely, money lost), provides a common consistent risk measure across different positions and risk factors, allows for sensible risk aggregation, and is holistic and probabilistic. It then reviews its limitations: it is “blind” to tail risks, does not satisfy the important property of subadditivity, can be unreliable when used for risk‐expected return analysis, and is vulnerable to “gaming” when used to control or remunerate traders. After discussing modern alternatives to the VaR, it addresses the (restrictive) circumstances in which a rational user might choose to use the VaR. These include the important case of probability‐of‐ruin problems, which include some capital allocation problems. It ends by briefly reviewing some of the common problems experienced by VaR users.
Expected Shortfall
Authors: Acerbi Carlo 
Published: May 2010

Abstract
Conditional Value at Risk (CV@R) and expected shortfall (ES) are synonymous terms defining a statistics of a random variable widely adopted as a portfolio measure of risk. It is the best‐known example of a coherent measure of risk, and is therefore a candidate alternative standard to Value at Risk for capital regulatory purposes. We discuss its definition, properties, and main applications.
Market Risk
Authors: Jorion Philippe 
Published: May 2010

Abstract
Modern risk management systems were developed in the early 1990s to provide centralized risk measures at the top level of financial institutions. In particular, Value at Risk (VAR) has become widely used as a statistical measure of risk based on current positions. Owing to the nature of this large‐scale aggregation problem, measuring VAR involves a number of choices and tradeoffs. VAR also has inherent limitations due to the fact that it provides a risk measure under normal but not extreme market conditions. Once put in place, however, the same risk architecture can be utilized to perform stress tests, which are essential risk tools. Generally, risk managers need to be aware of limitations in their quantitative risk models.
Commodity Forward Curve Modeling
Authors: Borovkova Svetlana 
Published: May 2010

AbstractIn this article, the important subject of commodity forward curve modeling is addressed. Forward curves are of paramount importance in commodity markets: they provide information about the views of market participants, anticipated price trends, and expectations about future supply and demand. Futures prices provide price discovery and are essential for daily marking to market existing portfolio positions. Moreover, futures prices provide the way of calibrating derivatives pricing models under the risk‐neutral probability measure. Here, an overview of forward curve models for nonseasonal commodities such as crude oil and seasonal commodities such as natural gas or agricultural commodities is given. Also, a brief outline on how these models can be estimated from the historical data and used for applications such as risk management and derivatives pricing is given.
Commodities and Numéraire
Authors: Geman Helyette , Shih Yih‐Fong 
Published: May 2010

AbstractThe goal of the article is to show that, in contrast to what has been sometimes stated, the behaviour of commodity prices over the last 19 years, namely a mean‐ reverting pattern during the nineties, then a remarkable rise during the period 2000–2008 and a collapse as of August 2008, is far from being solely explained by the moves of the dollar, the currency in which commodities are still denominated today. To make our point, we analyse three strategic commodities, crude oil, gold and copper, and show that the key features of the price trajectories remain essentially unchanged when using the dollar, the euro and the CRB index as the numeraire. On the other hand, the second part of the paper argues that the choice of the numeraire is crucial in the technical setting of options, plain‐ vanilla or complex, valuation in commodity markets and forward curve modelling.
Liquidity
Authors: Spatt Chester S. 
Published: May 2010

Abstract
We discuss the nature of liquidity as suggested by both market turmoil in 2007 and 2008 and classic academic treatments. A liquid asset is one that trades without significant movements in its price. We interpret liquidity in the context of the Kyle model, the no‐trade theorem, and adverse selection more broadly. We tie liquidity to volume and link this to whether there are close substitutes for the asset and whether liquidity is a priced‐factor. We also discuss liquidity provision, the self‐fulfilling nature of liquidity, coordination failures leading to illiquidity, and the transmission of illiquidity.
Execution Costs
Authors: Almgren Robert 
Published: May 2010

AbstractExecution costs can be a significant factor in overall investment performance, but are not straightforward to model and to measure. We discuss the three aspects of quantitative modeling of trade costs. For posttrade measurement, we discuss several different benchmarks in common use. For trade optimization, we discuss the construction of optimal trajectories to minimize cost and uncertainty. Finally, we discuss some of the issues in developing and calibrating pretrade cost estimation models.
Intraday Price Efficiency
Authors: Kelley Eric K. 
Published: May 2010

Abstract

Empirical methodologies used to assess intraday price efficiency are described. The metrics presented here summarize the extent to which actual prices deviate from an underlying efficient price and, therefore, attest to overall market quality. Two different approaches are discussed, and their relative merits are evaluated. The first approach uses a vector autoregression model over transaction‐based returns and trade information. The second one uses simple autocorrelations of intraday midquote returns. Because it explicitly decomposes price changes into permanent (efficient)
versus
temporary (pricing error) components and it is set in transaction time as opposed to clock time, the first approach is preferred.
G
losten–
M
ilgrom Models
Authors: Glosten Lawrence R. 
Published: May 2010

Abstract
Glosten‐Milgrom models analyze transaction prices arising from quotes of competing risk‐neutral dealers making a market in a single security and facing both privately informed and uninformed traders. The dealers must quote bid and offer prices at which they are willing to, respectively, buy and sell. A trader arrives and decides to buy, sell, or leave. Upon seeing the outcome of the trader's decision, the dealers modify their quotes in preparation for the next arrival. In the zero dealer profit equilibrium, private information induces a positive spread between bid and offer as the bid is the revised value of the security contingent on a sale. Since the quotes are revised expectations, transaction prices form a martingale. Specific examples illustrate the general results.
Kyle Model
Authors: Back Kerry , Baruch Shmuel 
Published: May 2010

Abstract
The Kyle model provides a tractable framework in which liquidity and the informativeness of prices can be measured. It has played a key role in research on heterogeneous information in financial markets. The model formalizes the relation of liquidity to the average rate of flow of new information. In this article, we review discrete‐time and continuous‐time versions of the Kyle model.
Roll Model
Authors: Nimalendran Mahendrarajah 
Published: May 2010

AbstractRoll's 1984 article “A Simple Implicit Measure of the Effective Bid–Ask Spread in an Efficient Market” developed a simple model to estimate the bid–ask spread using the serial covariance of observable trade prices. This model has been very useful in situations where the bid–ask spread was not directly available. More importantly, the model has been a foundation upon which several extensions and other models have emerged to estimate the spread and its determinants.
Automated Trading
Authors: Hendershott Terrence 
Published: May 2010

AbstractTechnology changes the way securities are traded. Both liquidity suppliers and liquidity demanders use computer algorithms to improve and automate their trading. Liquidity demanders attempt to minimize the price impact of a large order by dividing their order into small parts and executing it over time across multiple markets. Liquidity demanders do this to disguise the magnitude of their trading interest to prevent other market participants from capitalizing on their future trading demands. Liquid suppliers condition their quotes—buying and selling price schedules—on all available information. Technology allows more information to be processed more quickly. This should improve the efficiency of prices and allow for liquidity to be supplied at lower costs. While humans create and parameterize the algorithms used to trade, the actual trading process involves fewer and fewer humans.
Market Transparency
Authors: Foucault Thierry , Pagano Marco , Röell Ailsa 
Published: May 2010

Abstract
The article surveys theoretical and empirical work on the transparency of the securities trading process, distinguishing broadly between pretrade transparency (the display of quotes for prospective trades) and posttrade transparency (the publication of information regarding completed transactions). The impact of transparency on market liquidity, informational efficiency, and trading volume is reviewed, as well as the resulting gains and losses to different market participants.
Econometrics of Option Pricing
Authors: Renault Eric 
Published: May 2010

AbstractThe information content of a cross‐section of European option prices written on a given stock with a given time to maturity is summarized by the volatility smile. This article discusses how to graph the volatility smile, to interpret its asymmetry, convexity, term structure and time variation. Implied volatility, implied risk aversion, risk neutral valuation, and pricing kernels are discussed in the context of dynamic mixtures of geometric Brownian motions, possibly featuring stochastic volatility, long range dependence in volatility, and Poisson jumps. More general stochastic processes with possibly infinite activity jump processes as well as more data‐driven nonparametric approaches are also sketched.
Entropy‐Based Estimation
Authors: Kitamura Yuichi , Stutzer Michael 
Published: May 2010

Abstract
Efficient solutions to various estimation problems in financial modeling can be found by constrained optimization of entropy subject to linear constraints. Two such problems are the estimation of risk‐neutral probabilities needed for derivative security valuation and the estimation of parameters in econometric models amenable to general method of moments (GMM) estimation. The statistical theory of large deviations provides a frequentist interpretation of the entropy methods.
Risk Measures: Statistical Estimation
Authors: Gourieroux Christian 
Published: May 2010

AbstractThis article presents the main risk measures suggested in the current regulations for finance (Basel 2) and insurance (Solvency 2) to fix the reserves, which are the Value‐at‐Risk (VaR), Tail‐VaR, and the distortion risk measures (DRM). These measures can be used in a conditional or an unconditional framework. We explain how they can be estimated and give the distributional properties of the estimator. Finally, we interpret the selection of reserve levels as a control problem and explain how this interpretation can be used to check the methodologies proposed by banks or insurance companies to the regulators.
Realized Volatility and Multipower Variation
Authors: Andersen Torben G. , Todorov Viktor 
Published: May 2010

Abstract
This article reviews basic notions of return variation in the context of a continuous‐time arbitrage‐free asset pricing model and discusses some of their applications. We first define return variation in the infeasible continuous‐sampling case. Then we introduce realized measures obtained from high‐frequency observations which provide consistent and asymptotically normal estimates of the underlying return variation. The article discusses applications of these measures for reduced‐form volatility modeling and forecasting as well as testing for the presence of jumps.
Autoregressive Moving Average (ARMA) Processes
Authors: Brockwell Peter J. 
Published: May 2010

AbstractAutoregressive moving average (ARMA) processes {Yt,t = 0, ± 1, …} have played a key role as stationary models for time series observed at regularly spaced times. They constitute a very convenient parametric family, capable of exhibiting a broad range of dependence structures and marginal distributions. Well‐established prediction, model‐selection, and estimation techniques are also available and the asymptotic properties of the customary estimators are well understood. Continuous‐time ARMA (denoted CARMA) processes play an analogous role in continuous time. Although continuous‐time data is very rarely available, it is often the case that observations of a time series at discrete times can be fruitfully regarded as sampled values of an underlying continuous‐time process. The continuous‐time framework is very convenient for the modeling of high‐frequency data and for dealing with irregularly spaced discrete‐time data. Many of the problems of mathematical finance are formulated most conveniently in a continuous time setting, and in constructing more complex continuous‐time models for financial data, CARMA processes also play a role. Although ARMA and CARMA processes with infinite second moments can be defined we restrict our attention here to second‐order processes, for which these moments are finite. This article outlines the structure and essential properties of such processes.
Stylized Properties of Asset Returns
Authors: Cont Rama 
Published: May 2010

AbstractNonparametric or semiparametric statistical analysis of time series of financial asset—stock, index, exchange rate—returns has revealed a set of model‐free statistical properties, often expressed in qualitative terms, which are shared across a wide range of financial markets and instruments. We give an overview of these properties, commonly known as “stylized empirical facts”: unconditional and conditional distributions, tail properties, volatility clustering, and linear and nonlinear dependence of returns in time and across stocks.
Autocall
Authors: Roubinet Charles‐Henri 
Published: May 2010

Abstract
An equity‐linked autocallable note is a legal instrument in which the notional engaged by the customer is automatically reimbursed when the underlying stock reaches a strike at a specified recalling date or at maturity if such an event does not occur (when the recall appends a coupon is also paid to give the client a return on his/her capital higher than the one he/she would get from an investment in a bond). Because the date of the reimbursement of the capital is unknown, it is necessary to use a joint equity/interest rate model for the computation of the price and sensitivities of this product. Integrating the equity smile risk and the dividend risk can also be required, but it is much more complex with an interest rate factor: the local volatility formula does not hold anymore and convexity adjustments appear with fixed discrete dividends.
Asset–Liability Management
Authors: Ziemba William T. 
Published: May 2010

Abstract
Asset–liability management is a major concern for large financial institutions. Assets must be invested to achieve sufficient returns to pay liabilities and achieve goals subject to uncertainties, policy, taxes, and legal constraints. This article discusses asset and liability management with portfolio complexities and policy constraints. Applications to the management of investment portfolios for large financial institutions, including pension funds and insurance companies, and for individual life‐cycle planning are discussed. The approach recommended is discrete‐time, multiperiod stochastic programming. We present the Russell–Yasuda Kasai and the InnoALM models, both of which had a major impact on the practice of asset‐liability management (ALM).
Passport Options
Authors: Henderson Vicky 
Published: May 2010

Abstract

This article outlines the pricing and hedging of an exotic option called a
passport option
. The passport option was invented in the mid‐1990s by quantitative analysts at Bankers Trust and this falls into the more general class of products called
options on traded accounts
. The buyer of a passport option pays a premium and trades in an underlying asset (up to predefined limits). At expiry, the buyer receives any profit on this account, but is not responsible for losses. For this reason, the option has also been called a
perfect trader option
. In a general framework, the passport option is related to a lookback option, a “best price” option.
Reinsurance
Authors: Albrecher Hansjörg 
Published: May 2010

Abstract
In this article, the notion of reinsurance as a means for a first‐line insurer to pass on part of his underwritten risk for some appropriate premium payment is defined and motivated. Various forms of common reinsurance treaties of proportional and nonproportional types are described, including quota‐share, surplus, excess‐of‐loss, stop‐loss, and large‐claim treaties. Some actuarial and practical challenges in connection with the determination of suitable premiums for the reinsured risk are discussed. Subsequently, main obstacles in deciding upon the choice of the appropriate reinsurance form in a given situation are treated, which often can be expressed as an optimization problem with an objective function under constraints. Finally, connections between reinsurance and the realm of finance are discussed. Throughout the article, references to the literature and links to other articles are provided.
Cramér's Theorem
Authors: Tang Qihe 
Published: May 2010

AbstractFor a sequence of independent and identically distributed random variables whose moment‐generating function is finite in a neighborhood of the origin, Cramér's theorem gives a simple method to identify the exponential decay rate of the small probabilities that the empirical means are away from the population mean. In this article, we briefly review Cramér's theorem and related results in the context of large deviation theory.
Accumulated Claims
Authors: Schmidli Hanspeter 
Published: May 2010

Abstract

We consider models for the accumulated claim sizes, as they can, for instance, be used for modeling
operational risk
. A natural model consists of compound distributions. These models are difficult to handle. Modeling the accumulated claim sizes directly leads to simple approximations such as the normal approximation or the translated gamma approximation. Finally, numerical methods are successful for discrete compound distributions that are in the Panjer class of distributions.
Life Insurance
Authors: Steffensen Mogens 
Published: May 2010

Abstract
We give a survey of the mathematics of life insurance and some of its most important connections to quantitative finance. We model and valuate the payment stream of a life insurance contract on the basis of the insurance valuation principle, that is, diversification of risk. We discuss connections between this principle and the financial valuation principle of no arbitrage. We also see how quantitative finance helps in relaxing some of the strict assumptions on which diversification is based. We present different designs of contracts, including with‐profit life insurance and unit‐linked life insurance. They are classcial contract designs with so‐called participation features, that is, features that allow the policy holder to participate in the surplus of the insurance company or the capital gains on an investment portfolio. Finally, we discuss connections between the decision problems appearing from these contract designs and classical financial consumption–investment decision problems.