The MathFinance Newsletter, Edition 72, December 13
2002.
Previous editions and this edition in html format can be found on
http://www.mathfinancenews.com/.
In this issue:
- place a student
- recommend your book or educational institute
- find a quant
- invite to a workshop
- contribute to our website
- pose questions about mathematical finance
- introduce your research to a wider audience
The MathFinance Newsletter: Established November
1999
- supported by Landesbank Hessen-Thüringen -
Editor: Dr. Uwe Wystup, Frankfurt MathFinance Institute
Assistant Editor: Susanne Griebsch, Goethe-University, Frankfurt
Technical Editor: Tom Heide, University of Applied Science, Frankfurt
Database Solutions: Thorsten Schmidt, Giessen
University
In detail:
- MathFinance Job Exchange
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10 Researchers for E-Finance Project at Frankfurt and Darmstadt University DE-Hessen
Offers for
10 Researcher Assistants
(between 50% and 100% BAT IIa)
starting Jan. 1st, 2003
The Challenge
The E-Finance Lab Frankfurt a. M. was founded by Accenture, Deutsche Bank, Microsoft, Siemens and T-Systems in cooperation with Frankfurt and Darmstadt Universities. Our goal is to advance methods and to develop new information and communication systems supporting the imminent transformation process of the financial industry. Based on this, new revenue streams will be designed and evaluated, among others using prototyping and simulation techniques.
Beginning January 1st, 2003, we will work in these four topical clusters:
- Supply Chains in the Financial Service Industry, Business Intelligence and the Information Economy (head: Prof. Dr. Wolfgang König)
- Financial Supply Chain Management, Smart Selling and Standard Software (head: Prof. Dr. Bernd Skiera)
- Seamless Networking and Infrastructure Support for the Financial Services Industry (head: Prof. Dr. Ralf Steinmetz)
- Market vs. Hierarchy – Strategy, Products and Resources (head: Prof. Dr. Mark Wahrenburg)
Your work ought to guide companies of the financial sector to streamline their business and prototype new revenue streams while at the same time executing an impact on the scientific community, leading to high-quality research papers as well as an outstanding dissertation.
Your Profile
You finished your diploma or masters degree in Business, Economics, Information Systems, Finance, Marketing, Computer Science or Industrial Engineering as one of the best students of your graduation year. You have good methodological and formal skills, a profound background in Information Systems and Finance and experiences in developing and implementing information technology in the field. Ideally, you have an international experience (e. g., studies or apprenticeships) and you are highly interested in the fields of electronic finance.
For more information visit our website http://www.efinance-lab.com
Please submit your application in English to:
Prof. Dr. Wolfgang Koenig,
E-Finance Chair, Frankfurt University, Mertonstr. 17, D 60054 Frankfurt,
wkoenig@wiwi.uni-frankfurt.de -
Lectureship in Mathematical Finance at Imperial College Of Science, Technology And Medicine (University of London)
Applications are invited for a Lectureship in Mathematical Finance, to be appointed as soon as possible but not later than 1 October 2003.
The successful applicant will join the newly-formed Mathematical Finance Section in the Department, and will engage in research and specialist teaching for the MSc course in Mathematics and Finance, as well as contributing to the department's undergraduate teaching programme. Candidates will be expected to have proven research ability in some area of mathematical finance. Applicants should also be able to provide ancillary teaching to other departments within the College. While candidates may have backgrounds in stochastic analysis, finance, statistics or physics, some preference will given to those whose research interests include aspects of statistical data modelling and analysis. The appointment will be on the Lecturer scale of £29,621 to £33,679 p.a. plus London Allowance of £2,134.
The post is within the Department of Mathematics at Imperial College on the South Kensington campus.
Application forms are available from Mrs Doris Abeysekera (d.abeysekera@ic.ac.uk).
Mrs D. Abeysekera
Completed applications should include a CV, list of publications and names of three referees and should be sent to
Mathematics Department
Imperial College of Science, Technology and Medicine
180 Queen's Gate
London SW7 2BZ.
Further particulars can be obtained from the department's website (http://www.ma.ic.ac.uk). Informal enquiries can be made to Professor Mark Davis (mark.davis@ic.ac.uk, +44 20 7594 8486).
Closing date: 17 December 2002
The College is committed to equality of opportunity -
Master's in Financial Engineering Program at the University of California at Berkeley
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The Master's in Financial Engineering Program at the University of California at Berkeley is currently accepting applications for Spring 2004.
The MFE Program provides students with a one-year professional graduate degree from UC Berkeley's Haas School of Business. Instruction is led by world-renowned faculty from Haas, UCLA's Anderson School, and UC Irvine's School of Management.
Students in the MFE program learn to employ theoretical finance and computer modeling skills to make pricing, hedging, trading and portfolio management decisions. Courses and projects emphasize the practical applications of these skills.
Graduates of the Master's in Financial Engineering are prepared for careers in:
- Investment Banking
- Corporate Strategic Planning
- Risk Management
- Primary and Derivative Securities Valuation
- Financial Information Systems Management
- Portfolio Management
- Securities Trading
The final deadline for Spring 2003 has passed. We are now accepting applications for the MFE Class of 2005. Students admitted will begin classes in April 2004 and complete their degrees in March 2005.
Master's of Financial Engineering Program
Haas School of Business
University of California
Berkeley, CA 94720-1900
tel: (510) 642-4417
fax:(510) 643-4345
Contact Us
For information, please visit: http://mfe.haas.berkeley.edu
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The MFE Program is also seeking instructors for upcoming pre-program foundation math courses (30 hours each) which will be offered on an evening/weekend schedule in 2003-2004. Please note that the courses are not part of the MFE Program and instructors will not be part of the Haas Faculty.
Foundation Math Course
The Master's in Financial Engineering Program (MFE) at the Haas School of Business is offering a 30-hour foundation course that equips students with the mathematical background necessary in understanding the courses throughout the MFE Program. The course is composed of the areas of statistics/probability and (partial) differential equations used in contemporary finance practice. For truly advanced students the course may also serve as a refresher course.
The course will be taught by Dr. Domingo Tavella
Domingo Tavella, Principal of Octanti Associates, Inc., Ph.D. (engineering), Stanford University. Computational methods in financial pricing, stochastic simulation in finance and insurance, financial software development strategies and methods, risk management strategies in finance and insurance, hybrid insurance structures.
Please note that Dr. Tavella teaches quantitative courses in the MFE Program and hence is uniquely qualified to teach a targeted course in financial mathematics. The course will focus on preparing you for the rigorous math component of the MFE Program. Enrollment is limited.
Successful students will earn a certificate of completion from the Center of Executive Development (CED), Haas School of Business.
Course Description
Topics covered will include:
- Statistics, regressions, distributions, expectations, moments, and related concepts.
- Linear programming and related issues.
- Utility function concepts and applications.
Other topics like Monte Carlo, non linear optimization, and other numerical techniques will be discussed in an MFE Program course (Stochastic Calculus).
This course is unique in that it unites a number of fields that are the essence of strength of financial engineering methods, tailored for use in the MFE program.
Who Should Attend
Individuals interested in applying to the Haas Masters in Financial Engineering Program; those pursuing any quantitative analysis in the business world; those interested in actuarial science, or for those interested in seeing how mathematical theory can be applied in "real life."
Prerequisites
- Solid understanding of calculus, one dimensional and multi-dimensional.
- Good knowledge of ODEs.
- Exposure to PDEs.
- Solid knowledge of linear algebra, including eigenvalues, elementary optimization, and linear systems.
Course Fee and Registration
The course fee is $1,500 ($1,250 for those admitted to the MFE program).
For general information visit:
http://mfe.haas.berkeley.edu.
To be considered for this assignment, please contact Rachel Killian, MFE Associate Director at mfe@haas.berkeley.edu
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- MathFinance Events
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The Mathematics of Credit Derivatives by Prof. Philipp Schönbucher
Course Dates: 17th / 18th February 2003
Who should attend?
Course location: Central London
A 2 - Day course led by Prof. Philipp Schönbucher
- Counter-party risk
- Credit Derivatives
- Credit Research
- Credit Risk
- Financial Engineering
- Quantitative Analysis
- Risk Management
- Structured Finance
- Structured Credit Products
Course Leader: Prof. Philipp SchönbucherProf. Philipp J. Schönbucher is assistant professor of Quantitative Risk Management at the Department of Mathematics of the Swiss Federal Institute of Technology (ETH) Zurich. He holds degrees in mathematics (Oxford) and economics (Bonn) and a PhD in economics (Bonn). His publications include papers on credit risk modelling, credit derivatives pricing, stochastic volatility modelling, option pricing in illiquid markets, real options and term structure models. His main area of research is credit risk modelling and credit derivatives pricing in which he has been active since 1996. Philipp is a consultant and professional trainer to a number of leading financial institutions. Furthermore he is author of a book on "Credit Derivatives Pricing Models" (Wiley, 2003).
Aim of the course
This course covers the latest developments in the pricing and risk management of Credit Derivatives. The first day examines state-of-the-art techniques of modelling and hedging the risks of single-name credit derivatives, whilst in the second day you will learn the most recent developments in the modelling and pricing of portfolio and basket credit risks. Each major model is illustrated with a practical case study.
All cases studies use real-world data (quoted prices, CDS rates, historical default rates).
Course Programme Day 1
Single-Name Credit Derivatives:
9:00-10:30 Credit Derivatives: Instruments and Structures. Overview with an emphasis on payoffs, risks and simple hedge-strategies
10:30-11:00 Coffee Break
11:00-12:30 Spread-Curves and Intensity-based Models
12:30-14:00 Lunch Break
14:00-15:30 Dynamics in Spread Curves
15:30-16:00 Coffee Break
16:00-17:30 Firm’s value approaches: Hedging Credit with Shares: Does it Work?
Course Programme Day 2:
Basket- and Portfolio Credit Derivatives
9:00-9:45 Basket and Portfolio Credit Derivatives: Instruments and Structures
9:45-10:30 Pricing Multi-Name Credit Derivatives: Static Models
10:30-11:00 Coffee Break
11:00-12:30 Default dependency using the Gaussian Copula: Semi-dynamic Models
12:30-14:00 Lunch Break
14:00-15:30 Fully Dynamic Models
15:30-16:00 Coffee Break
16:00-17:30 Advanced Fully Dynamic Models
The Mathematics of Credit Derivatives 17th / 18th February 2003 Course fees
Standard fee per delegate:
£2295
(+ UK VAT @ 17. 5%)
Total cost: £2696.62
Discount:
When a second person attends from the same company, there is a 10% discount available on the second delegate booking. A third delegate booking from the same company promotes the 10% discount to incorporate the total fee.
Delegate details:
- Name:
- Position:
- Name:
- Position:
- Department:
- Address:
- Country:
- Phone:
- E mail
- Date:
- Signature:
Registration on :
Tel: +44 (0) 1273 674400
Fax: +44 (0) 1273 672333
Contact :
web : http://www.worldbusinessstrategies.com
Email : sales@worldbusinessstrategies.com
Flight details:
All delegates flying into London on the first morning of the event are reminded that the training starts at 9:00am sharp and delegates are requested to arrive at 8:30am GMT. The location is in Regents Park approximately 1 hour from all 3 main London airports, Heathrow, Gatwick and City. Returning flights should equally allow for the event finishing time approximately 5pm.
Hotel bookings:
World Business Strategies Ltd offer a discounted hotel booking service for all delegates at the events location: Sol Melia
White House Hotel
Albany Street
Regents Park
NW1 3UP
London
England
Contact Hotel Bookings +44 (0) 1273 674400
Sponsorship:
World Business strategies Ltd, offer sponsorship opportunities for all events, E-mail headers and the web site. Contact Sponsorship: +44 (0) 1273 674400
Disclaimer:
World business strategies command the rights to cancel or alter any part of this programme.
Cancellation:
By completing of this form the client hereby enters into a agreement that cancellation for a event must be made by fax of writing within two weeks of the event or no refunds shall be given. However in certain circumstances a credit note maybe issued for future events. Prior to the two-week deadline cancellations shall be subjected to a fee of 25% of the overall course costs. -
First Joint International Meeting between the American Mathematical Society and the Real Sociedad Matemática Española
The First Joint International Meeting between the American Mathematical Society and the Real Sociedad Matemática Española will be held in Seville (Spain) on June 18-21, 2003 The Conference program has six invited talks, 38 Special Sessions, and a session for "contributed papers". The Meeting will take place in the Escuela Técnica Superior de Ingenieros Industriales of the Universidad de Sevilla.
For more detailed information about the congress structure, please click on the General Information page.
One of the Special Sessions is entitled with "Mathematical Methods in Finance and Risk Management"
Length: 6 hours
Schedule: Wednesday(June 18):15.30-17.00//17.30-19.00
Friday(June 20): 10.00-11.00//11.30-13.30
Researches interested in presenting an abstract will be forwarded it to the organizers of the Special Session. Abstract acceptance will be done by the organizers of this Special Sessions, who will notify you of their decisions.
Period for submitting abstracts: From October 28th, 2002 to February 10th, 2003.
Organizers:
Santiago Carrillo Menendez, Universidad Autonoma de Madrid:santiago.carrillo@uam.es Antonio Falco Montesinos, Universidad Cardenal Herrera CEU:afalco@uch.ceu.es Antonio Sanchez Calle, Universidad Autonoma de Madrid:antonio.sanchez@uam.es Luis Seco, University of Toronto at Mississauga:seco@math.toronto.edu
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- MathFinance Resources
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Pricing and Hedging of Derivative Securities by Lars Tyge Nielsen
Textbook in continuous-time finance theory, published by Oxford University Press, 1999.
Intended readership
The book is an introduction to the theory of pricing and hedging of derivative securities in continuous time for graduate and advanced undergraduate students and for researchers in both academia and the financial industry. It is suitable as a text in graduate (postgraduate) and advanced undergraduate courses not only in finance and economics programs, but also in mathematical finance, statistics and mathematics programs.
Design
The material and the exposition have been thoroughly tested in doctoral courses at INSEAD, New York University, and Columbia University, and in executive courses in derivative securities pricing at the Amsterdam Institute of Finance. Innumerable comments and questions from students and colleagues have been incorporated, explained, and answered in succesive revisions.
The level of mathematics preparation required by the reader is even. The book does not assume that the reader is already an expert in the mathematics. The necessary mathematical machinery is developed in a precise and rigorous manner, while unnecessary mathematics is avoided. A lot of effort has gone into deciding what to include and what not to include.
Where the book does not provide complete proofs of a theoretical or mathematical result, it gives a reference to where a complete proof can be found. It defines all the necessary concepts and states all the necessary results in a precise manner. It explains the intuition behind those concepts and results, how they fit in to the finance theory, and why they are necessary.
For students and teachers of finance and economics
The theory of continuous-time stochastic processes is an essential prerequisite for continuous-time finance. It is not easily accessible, and it has for a long time formed a barrier of entry into the field. One purpose of this book is to help break down that barrier and make it possible for the reader actually to learn this material.
Finance instructors often refuse to teach the mathematics behind derivative securities pricing. They either "assume" that the students already know it (the way economists assume a can opener), or they ask them to go take courses in the mathematics or statistics department in order to learn it.
If the math courses are not designed with a view to mathematical finance, then all but the most talented and motivated finance students will lose their motivation and their bearings.
This book offers finance instructors the opportunity to teach and learn the necessary mathematics in a way that is intimately related to the derivative securities applications. Alternatively, those who do not wish to teach mathematics can go directly to the financial economics chapters while using the mathematical chapters for review purposes.
The book has been used in one-semester courses with excellent results, but a better idea might be to stretch it over two semesters. In that case, it could be supplemented with survey-style coverage of topics that are not included in the book (survey-style material on derivative securities can be found in many other books) as well as in-depth coverage of the instructor's own favorite issues.
For students and teachers of mathematical finance and financial engineering
Mathematics instructors may wish to fill in some of the proofs that have been skipped in the text and to supplement with more advanced and difficult material. However, they will benefit pedagogically from sticking to the structure of the text, and they are advised to exercise restraint in supplementing it.
Once the students have learned the mathematics and the applications in the book, they will be much better motivated and prepared to study the most advanced material, both in mathematics and in finance.
For students and teachers of stochastic calculus
Teachers of stochastic calculus who recognize the pedagogical and motivational value of applications might consider structuring a course around this book or using the book as a supplement to their primary materials.
The fundamental material is covered
Two theoretical chapters cover price processes and trading strategies, prices of risk and state price processes, arbitrage, replication, delta hedging, dynamic market completeness, and the martingale valuation principle, with examples and exercises scattered throughout. The treatment of the fundamental theory of derivative securities pricing is detailed and extensive.
Two applications chapters analyze the Black-Scholes model and the one-factor Gaussian term structure models in detail.
Every chapter has a summary which explains and reviews the chapter and the intuition behind it in a mix of common sense and technical terms. There are also critical notes on the literature at the end of each chapter.
There are exercises scattered throughout the book, and there are suggested solutions of all of them. Doing exercises is a very helpful, even indispensable, part of the learning process.
You get the necessary background in stochastic process theory
Dynamic information structures, measurable and adapted processes, Wiener processes, geometric Brownian motion, stochastic integrals, Ito processes, Ito calculus with plenty of examples, Girsanov's Theorem, the Martingale Representation Theorem, Gaussian processes such as Ornstein-Uhlenbeck processes and Brownian bridges.
All this mathematics is absolutely necessary for mastery of the pricing and hedging of derivative securities. The book explains why it is necessary and makes it easy for you to learn.
There are also two appendixes about measure and integration theory and one about the heat equation. You can read them or just use them as a reference.
The book answers all these intriguing questions about the theory
- Do trading strategies really have to satisfy some kind of square integrability condition?
- How exactly are the state price process, the interest rate, the prices of risk, and the risk adjusted probabilities related to each other?
- What is the relationship between the state price process and the Hansen-Jagannathan bounds?
- How do we deal with the Harrison-Kreps doubling strategy, which shows that arbitrage is always possible in the Black-Scholes model, multitudinous claims to the contrary notwithstanding?
- Why did Harrison and Pliska abandon their idea of requiring the value processes of self-financing trading strategies to be bounded below?
- When Cheng showed that the Ball-Torous model is not arbitrage free, was that the same point that Harrison and Kreps made or was it a different one?
- What was Merton's Nobel prize winning argument about absence of arbitrage, and how does it square with Harrison and Kreps?
- What was the subtle point about complete markets made by Mueller and elaborated by Jarrow and Madan?
- Does the risk adjusted probability distribution have to be uniformly absolutely continuous with respect to the original probabilities?
- Is it necessary to assume that the density of the risk adjusted probability distribution is square integrable?
- Does the Black-Scholes partial differential equation have a unique solution?
Of course, you will also get the standard stuff
Price processes, trading strategies, the budget constraint, interest rates, prices of risk, their existence and uniqueness, state price processes, arbitrage, changing the unit of account or the numeraire, replication of claims, delta hedging, dynamic market completeness and the complete markets theorem, the martingale valuation principle using either the state price process or the risk adjusted probabilities, and lots of examples.
Comprehensive analysis of two important applications
Would you like to see, once and for all, a comprehensive analysis of the Black-Scholes model and the Black-Scholes Formula?
- Do we really know that the value function of a claim is sufficiently differentiable to apply Ito's Lemma?
- How is the volatility of a claim related to its elasticity?
- How can the elasticity be interpreted in terms of the leverage of the replicating portfolio?
- Do these observations apply only to standard options or also to more fancy claims?
- In what sense does the value of a cash-or-nothing call option converge to the payoff as the time to maturity goes to zero, and in what sense does it not so converge?
- What is the trick that allows easy calculation of the partial derivatives (the Greeks) of the Black-Scholes Formula?
- Where does gamma of a call option reach its maximum, at the money, at the money relative to the forward price, or somewhere else?
- Why does the value of the call option approach the value of the underlying when volatility goes to infinity?
- How can you go back and forth between the Black-Scholes partial differential equation and the heat equation?
- What is the boundary condition that should be imposed, and how should it be imposed?
And how about a detailed exposition of all the one-factor Gaussian term structure models? A derivation of the models based on the martingale valuation principle, and a mathematical analysis of their qualitative features, illustrated by plenty of graphs? Get to understand these models really well, so that you can use them as a reference point when you deal with more complicated models.
- How can the extended Vasicek model, the simplified Hull-White model and the continuous-time Ho-Lee model be calibrated?
- What is the relation between the forward rate risk premium and the yield risk premium?
- What is the shape of the bond price volatility curve in the Vasicek model and in the simplified Hull-White model?
- What about the Merton model and the continuous time Ho-Lee model?
- What are the shapes of the forward rate standard deviation curves in these models?
- The zero coupon yield standard deviation curves?
- What are the possible shapes of the yield curves in the Vasicek model and in the Merton model?
- How are these shapes affected by the model parameters?
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Cross Currency Swap
A Cross Currency Swap is an agreement between two parties to exchange interest payments denominated in two different currencies for a specified term. One interest payment is typically calculated using a floating rate index such as USD LIBOR. The other interest payment is based upon a fixed rate or another floating rate index denominated in a different currency.
Unlike a single currency swap, a Cross Currency Swap sometimes (but not always) involves an exchange of principal. The initial principal exchange occurs at the beginning of the swap with a re-exchange at maturity. The principal amounts are based on initial spot exchange rates.
Example
Suppose a manufacturer, XYZ Company, is building a new plant in Germany using term fixed rate financing. Suppose further that XYZ, having little access to the German capital markets, concludes that borrowing US Dollars from a domestic bank offers the most cost-effective source of financing. Additionally, the domestic loan will be based on floating rate LIBOR for a 7 year term.
XYZ can fund in US Dollars (USD) and then convert to Deutsche Marks (DM) using a Cross Currency Swap. XYZ will make an initial exchange of USD for DM at the current spot exchange rate with an agreement to re-exchange at the same rate when the swap terminates in 7 years. In this way, the company is not exposed to exchange rate risk when closing out the swap and paying down the loan.
During the life of the swap, the DM interest payment due from the company is tied to an agreed upon fixed rate while the USD amount paid to their counterparty is tied to LIBOR. The LIBOR interest payment that XYZ receives will offset the LIBOR based payment on the loan. In effect, the company is left with a fixed interest payment based on a fixed DM amount. This payment is funded by DM cash flow from the new plant. In sum, XYZ is insulated from both exchange rate and interest rate risk.
This is taken from http://us.hsbc.com/corporate/treasury/derivatives/crossswap.asp -
Levy Processes in Finance: Pricing Financial Derivatives, written by Wim Schoutens
John Wiley & Sons, Ltd publishes a wide range of scientific, technical and medical books and journals. One particular publication, Levy Processes in Finance: Pricing Financial Derivatives, written by Wim Schoutens, carries information of direct relevance to the visitors to this website.
Levy Processes in Finance : Pricing Financial Derivatives
Wim Schoutens
ISBN: 0-470-85156-2
Hardcover
208 Pages
April 2003
£45.00 / €74.30 Add to Cart
Table of Contents
Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of Lévy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. Lévy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of Lévy-based models, and features many examples of how they may be used to solve problems in finance.
- Provides an introduction to the use of Lévy processes in finance.
- Features many examples using real market data, with emphasis on the pricing of financial derivatives.
- Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling.
- Includes many figures to illustrate the theory and examples discussed.
- Avoids unnecessary mathematical formalities.
The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers.
If you would like more information on the book, please visit:
http://www.wileyeurope.com/cda/product/0,,0470851562,00.html -
Finance and Stochastics Volume 7 Issue 2
- Paul Embrechts, Andrea Hoeing, Alessandro Juri:
Using copulae to bound the Value-at-Risk for functions of dependent risks - Huyên Pham:
A large deviations approach to optimal long term investment - Thomas Møller:
Indifference pricing of insurance contracts in a product space model - Jianming Xia:
Dividing gains between a client and her agent - Per Hoerfelt:
Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou - Wendell H. Fleming, Daniel Hernandez-Hernandez:
An optimal consumption model with stochastic volatility - Michal A. H. Dempster, Igor V. Evstigneev, Klaus R. Schenk-Hoppe:
Exponential growth of fixed-mix strategies in stationary asset markets
http://link.springer.de/link/service/journals/00780/tocs/t3007002.htm
or
http://link.springer-ny.com/link/service/journals/00780/tocs/t3007002.htm - Paul Embrechts, Andrea Hoeing, Alessandro Juri:
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