Talks in Financial and Insurance Mathematics, Winter 2001/02

• Dr. Richard B. Olsen (Olsen Daten AG)
  The inside of currency markets
  
  Abstract: Currency markets are the most efficient markets in the world with a daily transaction volume of 1.5 trillion USD, which is fifty times larger than the volume of all equity markets taken together. Historically, market making in currency markets has been done by practitioners and has not been automated. Oanda FXTrade is a new foreign exchange trading platform, where the whole process of market making has been automated. The platform offers an inside view of the dynamic behaviour pattern of traders. The seminar discusses some of the key issues in understanding the dynamics of currency markets and outlines the use of a model to automate the market making process.

• Tom Passante (Swiss Re)
  Application of regression based reserving methods to reinsurance pricing
  
  Abstract: Traditional actuarial methods for projecting ultimate loss burdens are based on loss development methods (a.k.a. link-ratio methods) which are applied to basic loss triangles. In this presentation, a regression based method is introduced and briefly discussed, and is used to show that the traditional methods can often times be flawed. Pertinent information which is present in the triangle can be lost using the traditional methods, but is recovered through use of regression methods. However, regression methods are not always recommended, since they also contain their own weaknesses. This presentation will discuss the advantages and disadvantages of regression based methods over the traditional loss development methods.

• Prof. Dr. Phelim Boyle (University of Waterloo, Canada)
  Asset allocation: finding the right weights
  
  Abstract: An oft quoted rule of thumb states that a pension plan should maintain sixty percent of its funds in stocks and the rest in bonds. This is certainly a simple rule but can it capture the dimensions of the asset allocation decision? This decision is critical for investment managers of pension plans, mutual funds and other financial institutions. In recent years institutions have increasingly passed the allocation choice down to the individual investor: witness the rise of defined contribution pension plans and the bewildering array of different types of retail investment products. We suggest that modern finance can assist the investor in this decision. There has been considerable theoretical progress in this problem in recent years and the martingale approach developed by Cox and Huang, Pliska and others provides a useful line of attack. In this talk we discuss the numerical implementation of some recent approaches and describe preliminary research that uses the Monte Carlo method to estimate the optimal portfolio weights.

• Prof. Philip Protter (Cornell University, NY)
  The Longstaff-Schwartz algorithm actually works
  
  Abstract: Recently F. Longstaff and E. Schwartz proposed a Monte Carlo method for the computation of American option prices, in financial asset pricing theory. This algorithm involves two types of approximation. First one replaces the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Second, one uses Monte-Carlo simulations and least squares regression to compute the value function of the approximation from the first step. Under fairly general conditions, we will sketch how one can obtain the almost sure convergence of the complete algorithm. We also determine the rate of convergence of the second step, obtaining a Gaussian asymptotic normalized error. The talk is based on joint work with E. Clement and D. Lamberton.

• Prof. Dr. Walter Schachermayer (TU Wien)
  The Fundamental Theorem of Asset Pricing under proportional transaction costs in finite discrete time
  
  Abstract: We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a d x d matrix-valued stochastic process (S_t)_t=0,...,T specifying the mutual bid and ask prices between d assets.
     We introduce the notion of "robust no arbitrage", which is a version of the no arbitrage concept, robust with respect to small changes of the bid ask spreads of (S_t)_t=0,...,T. Dually, we interpret a concept used by Kabanov and his co-authors as "strictly consistent price systems". We show that this concept extends the notion of equivalent martingale measures, playing a well-known role in the frictionless case, to the present setting of bid-ask processes (S_t)_t=0,...,T.
     The main theorem states that the bid-ask process (S_t)_t=0,...,T satisfies the robust no arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Dalang-Morton-Willinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker.
     An example of a 5 x 5-dimensional process (S_t)_t=0,...,T shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the so-called strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker.

• Prof. Dr. Elisaveta Pancheva (Institute of Mathematics and Informatics, BAS, Sofia)
  Relationsship between extremal processes and processes with additive increments generated by the same point process
  
  Abstract: A Bernoulli point process (B.p.p.) is simple in time, it has Radon mean measure and its restrictions to disjoint sets are independent. Given a sequence of B.p.p's N_n = {(T_nk,X_nk) : k >= 1} on the strictly positive quadrant of R^d+1, one associates with each N_n both the sum process S_n(t)  of all X_nk with k satisfying T_nk <= t and the extremal process Y_n(t), defined as maximum of all X_nk satisfying T_nk <= t. We are interested in the relationship of the convergences of N_n to N, S_n to S and Y_n to Y in case of independent X_nk.
     The complicated relation between an extremal process and the underlying B.p.p. in the multivariate framework is treated in [1]. The connection between the associated sum and extremal process in the univariate case is described in [2]. The multivariate picture may be unpleasantly disturbed by the lower curve of the extremal process.
     In the case of increasing sum and maxima we use time-space changes (\tau_n(t),u_n(x)) as norming mappings, strictly increasing and continuous in each coordinate, and study the limit behaviour of S_n and Y_n associated with the B.p.p. {(\tau_n(T_k),u_n(X_k)) : k >= 1}. Under certain conditions the limit extremal process is compound self-similar [3]. We study the connection between its exponent measure and the Levy measure of the limit sum process.
  References
  1. A.A.Balkema, E.I.Pancheva (1996). Decomposition for multivariate extremal processes. Commun. Statist.- Theory Meth., 25(4), 737–758.
  2. S.I.Resnick, M.Rubinovich (1973). The structure of extremal processes. Adv. Appl. Probab. 5, 287–307.
  3. E.I.Pancheva (1998). Self-similar extremal processes. J. Math. Sci., 92(3), 3911–3920.

• Prof. Dr. Walter Schachermayer (TU Wien)
  Nutzenmaximierung in unvollständigen Finanzmärkten
  
  Abstract: We give a review of classical and recent results on maximization of expected utility for an investor who has the possibility of trading in a financial market. Emphasis will be given to the duality theory related to this convex optimization problem.
     For expository reasons we first consider the classical case where the underlying probability space is finite. This setting has the advantage that the technical difficulties of the proofs are reduced to a minimum, which allows for a clearer insight into the basic ideas, in particular the crucial role played by the Legendre-transform. In this setting we state and prove an existence and uniqueness theorem for the optimal investment strategy, and its relation to the dual problem; the latter consists in finding an equivalent martingale measure optimal with respect to the conjugate of the utility function. We also discuss economic interpretations of these theorems.
     We then pass to the general case of an arbitrage-free financial market modeled by an R^d-valued semi-martingale. In this case some regularity conditions have to be imposed in order to obtain an existence result for the primal problem of finding the optimal investment, as well as for a proper duality theory. It turns out that one may give a necessary and sufficient condition, namely a mild condition on the asymptotic behavior of the utility function, its so-called reasonable asymptotic elasticity. This property allows for an economic interpretation motivating the term "reasonable". The remarkable fact is that this regularity condition only pertains to the behavior of the utility function, while we do not have to impose any regularity conditions on the stochastic process modeling the financial market.

• Awarding of the Walter Saxer Insurance Prize
  
  

  Winner	Daniel Brönnimann (D-Math, ETHZ) for his diploma thesis "Die Entwicklung des Wahrscheinlichkeitsbegriffs von 1654 bis 1718".
  Laudatio	Prof. Dr. Frank Hampel (Seminar for Statistics, ETH Zürich)
  Talk	Jon Bardola (Zurich Insurance) An asset liability management project in life insurance Abstract: We describe a pilot project, which has been successfully completed in Switzerland. It should give answers to important questions for managing a life insurance company, in particular during a low interest rate environment or after a drop in stock markets: "For how much longer can high policyholder returns be supported? Do we have an optimal investment strategy and how risky is our strategy? Which investment- and policyholder bonus-strategy will extract maximum value?" In the first part we will explain how this model has been built up (stochastic and dynamic modeling). In the second part we will discuss some results (return measures, investment strategies, bonus strategies).
  Apero	Dozentenfoyer of ETHZ (offered by Zurich Insurance)

• Dr. Jochen Maurer (Time-Steps)
  Pricing and risk analysis of energy portfolios
  
  Abstract: In open electricity markets the competition on the saturated market leads to significant retail price decreases. On the same time, the volatility of the prices and the uncertainty of the returns increases. Hence, electricity utilities have to ensure their power supply and retail prices against market risks. To improve their performance, modern risk management skills, like risk-based valuation and risk capital management, have to be applied.
     To handle an energy portfolio, one tries to find relationships between the power and financial markets: The power plants and electricity contracts are linked to instruments known from the financial markets, like for instance European or American options. The stocks of the financial market are mapped to energy commodities of a power market.
     We will discuss briefly the related characteristics in the power and financial markets and present a numerical simulation tool, which allows for the pricing and risk analysis of an energy portfolio. The tool is split up into three parts:
  1. Modeling of the power market using the full correlation structure between the commodities
  2. Risk-based valuation of risk components: Pricing of highly exotic financial instruments using analytical solutions and numerical integration methods
  3. Calculation of risk measures and risk capital needs, like for instance the Value-at-Risk of single contracts or the whole portfolio

• Prof. Dr. Claudia Klüppelberg (Department of Mathematics, TU Munich)
  Mathematische Theorie der Rekorde

• Prof. Martin Schweizer (Department of Mathematics, University of Munich)
  The value of investment information
  
  Abstract: Consider an investor in a financial market who has the opportunity to purchase some information at a given date. Since the additional information leads to better investment decisions, it is clear that there will be a price to pay for it. But how much? We address this question by means of a utility indifference approach. In mathematical terms, this involves enlargements of filtrations, measure changes and martingale representation results. We present some general theory as well as a number of examples. This is joint work with D. Becherer and J. Amendinger.

• Dr. Dirk Becherer (TU Berlin)
  PDE-solutions for rational hedging and valuation under constant absolute risk aversion
  
  Abstract: If contingent claims integrate tradable and untradable sources of risk, perfect hedging becomes impossible and the issuer's valuation and his partial hedging strategy have to depend on his attitudes towards risk. We study a rational valuation and hedging principle for such claims. It is based on the preferences of a rational investor with constant absolute risk aversion, and uses exponential utility indifference arguments. In a dynamical financial market framework, this idea was studied by several authors recently. The problem is well understood on a general abstract duality level, but more explicit solutions are limited so far.
     Our focus in on constructive results and properties of the utility indifference price and a corresponding hedging strategy. To this end, a new incomplete model is developed which is driven by a Markovian system of SDEs. It allows for a variety of mutual stochastic dependencies between the tradable asset prices and additional untradable factors of risk on the one hand, but nevertheless still permits for a fairly explicit solution: In analogy to the Black-Scholes model, both the utility indifference price and the hedging strategy can be described by the solution to a partial differential equation, but the untradable factors of risk demand for an interacting non-linear system. To illustrate the results, we discuss some applications at the interface of finance and insurance, like equity-linked insurance contracts, credit risk and weather derivatives.

Abstract: The discretisation of stochastic procesess in financial applications is quite important. Most financial models are continuous time models, whereas the real world only offers the possibility to trade in discrete time. Also from a numerical viewpoint, the calculations can only be done in a discrete framework. The minicourse will treat some problems that come from the approximation of continuous time processes with discrete processes.

• Prof. Dr. Rajna Gibson (Swiss Banking Institute, University of Zürich)
  Modern Finance: Is it not strange that desire should so many years outlive performance (Henry IV, part II, W. Shakespeare)

• Dr. Yves Achdou (Paris)
  On some partial differential equation from finance
  
  Abstract: The topic is the numerical solution of the Black-Scholes equation coupled with a stochastic volatility model.

• Dr. Chris Kenyon (IBM Zurich Research Laboratory)
  A multi-factor forward price model for network-based commodities
  
  Abstract: We introduce a multi-factor forward price model for network-based commodities such as point-to-point telecommunications capacity. The model explicitly includes network effects and the requirement that tradeables (forward contracts) be martingales under an appropriate measure. In essence the forward price model is a combination of network optimization and mathematical finance. The model is based on a modified HJM approach with additional compensators to include network effects and the martingale requirement. We show that the combination of network effects and martingale requirements on forward contract prices changes price volatility, observed standard deviations and, consequently, option prices. The effect of the network is always significant but the importance of the topology itself is variable. For typical volatilities European call option values are roughly 10% to 60% less in a network context for 1 year maturities for at-the-money and above strike prices respectively. The significance for more exotic and specially designed options, e.g. alternative-path barrier options, may be even higher.

• Dr. Mario Wüthrich (Winterthur)
  Korrelationen und Copulas
  
  Abstract: Wir werden sehen, dass in den meisten Beispielen der Begriff der Kovarianz versagt, um Abhängigkeiten in den Tails zu beschreiben. Aus diesem Grund werden wir Copulas einfuehren. Copulas sind mehrdimensionale Verteilungen auf dem Einheitswürfel, deren Randverteilungen alle uniform auf [0,1] sind. D.h. indem man alle Effekte der Randverteilungen eliminiert, erhält man eine mehrdimensionale Verteilung, welche es erlaubt, die inneren Abhängigkeitsstrukturen zu studieren.

• Prof. Glenn Shafer (Rutgers University, Newark NJ)
  Game-theoretic probability
  
  Abstract: In our recent book, Probability and Finance, Volodya Vovk and I show how game theory can replace measure theory as a foundation for mathematical probability, and how stochastic assumptions can be eliminated in finance. This talk illustrates these points with examples: the game-theoretic central limit theorem and the game-theoretic Black-Scholes formula. (Notes for the talk can be downloaded from http://www.andromeda.rutgers.edu/~gshafer/publec.htm; Lecture 1.)

• Empirical investigation of market liquidity
• Dynamical calculation of value-at-risk
• Quantification of operational risk according to Basle II

• Dr. Uwe Schmock (ETHZ and Swiss Banking Institute, University of Zürich)
  Term structure models for credit risks
  
  Abstract: This talk gives an overview on the available theoretical methods for pricing defaultable bonds. We review popular models for the term structure of risk-free interest rates, introduce hazard rates and loss fractions and thereby motivate default-adjusted interest rates. Several modelling assumptions for recovery at default are mentioned. We proceed by discussing the term structure of credit spreads and their dependence on risk-free interest rates. We conclude with remarks on the modelling of dependent defaults.

• Prof. Christophe Stricker (Université de Franche-Comté, Besançon)
  The fundamental theorem of asset pricing under proportional transaction costs
  
  Abstract: We consider a multi-asset discrete-time model of a financial market with proportional transaction costs and efficient friction and prove necessary and sufficient conditions for the absence of arbitrage. Our main result is an extension of the Dalang-Morton-Willinger theorem. As an application, we establish a hedging theorem giving a description of the set of initial endowments which allow to super-replicate a given contingent claim.

• Jean-Luc Vuarnoz (Swiss Life)
  Underwriting und Antiselektion in der Personenversicherung
  
  Abstract: Anhand zahlreicher Beispiele aus der Praxis wird die Antiselektion illustriert. Die Zusammenhänge zwischen Antiselektion und Produktdesign einerseits und Risikoprüfung andererseits werden verdeutlicht. Kommende Herausforderungen im Gebiet Risikoprüfung, z.B. Internet-Verkauf und Gentests, werden kurz diskutiert.

• Dr. Thorsten Rheinländer (Department of Mathematics, ETH Zürich)
  A martingale duality approach to stochastic volatility models
  
  Abstract: We discuss the valuation of derivatives in a general stochastic volatility context. The fact that the volatility typically is unbounded already rules out several well known approaches to valuation in incomplete markets. It turns out that it is still possible to follow a minimal entropy approach. We determine explicitly the resulting pricing measure for some classical stochastic volatility models and provide general verification results.

• Prof. Michael Taksar (Department of Applied Mathematics, State University of New York at Stony Brook)
  Ruin probabilities minimization and dividend distribution optimization in diffusion models
  
  Abstract: We consider a large insurance company whose surplus can be modeled by a diffusion process. Under different reinsurance schemes - proportional, excess-of-loss, XL-reinsurance, we study the problem of ruin probability minimization and dividend distribution maximization.
     We look at the cases with and without a possibility to invest the surplus in the financial market. In the former case an interesting phenomenon can be observed. If one optimizes the "public good" by minimizing the ruin probability, then the reinsurance control and the financial investment control must be done in tandem. On the other hand, optimization of the "welfare of the shareholders" results in a qualitatively different type of behavior, when one first deals with the reinsurance and then with the investments.

• Prof. Dr. Giovanni Barone-Adesi (City University, London, and USI Lugano)
  Stock valuation and investments: Analysis, state of the art and practical implications

• Prof. Stavros A. Zenios (University of Cyprus and Wharton School, University of Pennsylvania)
  Dynamic portfolio optimization for tracking corporate bond indices in an integrated market and credit risk environment
  
  Abstract: The management of credit risky assets requires simulation models that integrate the disparate sources of credit and market risk, and suitable optimization models for scenario analysis. In this paper we integrated Monte Carlo simulation models with dynamic portfolio optimization models and apply them to the tracking of corporate bond indices. Results show that good tracking performance can be achieved by a strategic model, however extra value may be generated with a models that goes down to the tactical level with bond picking decisions. Credit-risky and derivative securities can be incorporated in a government bond portfolio. Extensive empirical results with the ex post performance of the model over an eighteen month recent period substantiate the conclusions of this paper.

• Dr. Philipp J. Schönbucher (Department of Statistics, University of Bonn)
  Pricing basket credit derivatives with copula-dependent defaults

• Dr. Hyejin Ku (University of North Carolina at Charlotte)
  The consistency of two markets

• Dr. Ali Hirsa (Morgan Stanley, New York)
  Credit spreads implied from option markets
  
  Main topics:
  • Calibrating risk neutral processes from options data
  • The Merton default model revised
  • Equity dependent hazard rate approach
  • Option implied credit spreads using EDH
  • Conclusion and future work
  (Joint work with Dilip B. Madan)

• Dr. Damir Filipovic (Department of Mathematics, ETH Zürich)
  Affine processes and applications in finance
  
  Abstract: An affine process (AP), X, is a Markov process with the property that, for every t, the characteristic function of X_t has exponential-affine dependence on the initial state X₀. We provide a complete characterization of APs and exploit their rich structural properties. APs have been extensively used in financial modelling, both for their tractability and for their flexibility in capturing many of the empirical features of financial time series. We give a sketch of some applications including: the term structure of interest rates, the pricing of options and credit risk. (Joint work with D. Duffie and W. Schachermayer.)

• Dr. Ali Hirsa (Morgan Stanley, New York)
  Pricing American options under variance gamma
  
  Abstract: We derive a form of the partial integro-differential equation (PIDE) for pricing American options under variance gamma (VG) process. We then develop a numerical algorithm to solve for values of American options under variance gamma model. In this study, we compare the exercise boundary and early exercise premia between geometric VG law and geometric Brownian motion (GBM). We find that GBM premia are understated and hence we conclude that further work is necessary in developing fast efficient algorithms for solving PIDE's with a view to calibrating stochastic processes to a surface of American option prices. (Joint work with Dilip B. Madan.)

• Prof. Dr. F. Thomas Bruss (Département de Mathématique, Université Libre de Bruxelles)
  High-risk investment models
  
  Abstract: After a short examination of some characteristics of high-risk investments we focus our interest on the following question: How should we invest capital into a sequence of investment opportunities, if we want to invest in an opportunity which turns out best in a given horizon.
     We introduce several variations of models to study this question. Viewing high-risk situations we assume that an investment on the very best opportunity yields a lucrative, possibly time-dependent, rate of return, whereas each "wrong" investment loses its value. Uninvested capital may either keep its value, or, alternatively, be lost. The objective is to maximize the corresponding expected return. Several models are presented, mainly for the so-called rank-based case. We first treat the case of a fixed number of opportunities. Optimal strategies and values are found, also for different utility functions, leading to different forms of optimal strategies. To add to the applicability we then look for tractable models for an unknown number of opportunities. This case is in general much harder but a modelisation via some special processes is shown to be worth considering and to allow for explicit solutions.
     Parts of this talk are based on joint work with Thomas S. Ferguson (UCLA).
  
  Keywords: venture capital, targeted investment, odds-algorithm, secretary problems, Kelly betting system, general utility, optimality principle, differential equations, Euler-Cauchy approximation, Pascal processes

• Dr. Jesper Lund Pedersen (RiskLab, Dept. of Math., ETH Zürich)
  Optimal selling rules for stock trading
  
  Abstract: The focus of this talk will be on two optimal prediction problems. The two problems will be interpreted as timing to sell a stock. Thus, the two objectives are to maximize the following: i) The probability that the stock price is greater than a given percentage of the ultimate maximum price over a given time period. ii) The probability that the difference (error) between the ultimate maximum price over a given time period and the stock price is less than a given value.

• Dr. Jeffrey Collamore (RiskLab, Dept. of Math., ETH Zürich)
  Multidimensional risk processes and large deviations
  
  Abstract: In the classical ruin problem of collective risk theory, an insurance company gains capital from premiums income and looses capital as a result of claims; one then studies the probability that the company's total capital ever falls below zero, i.e., P{S(t) < -m, for some t}, where S(t) is a positive-drift Lévy process and m is the company's initial capital.
      In this talk, I will discuss various generalizations of this problem to higher dimensional settings. The first of these can be described as follows: Let S(1),S(2),... be a sequence of random vectors, corresponding e.g. to several capital factors, and consider the probability that this sequence ever reaches some "forbidden region" in d-dimensional Euclidean space. It will be shown that, under quite general assumptions,
  
  
  (*)     (1/m) log P{S(n) ever hits mA} ~ -J(A)
  
  for an appropriate "rate function" J(A). Some refinements, describing e.g. the asymptotic distribution of the first passage time, will also be given.
      A second generalization which will be discussed is the case where the increments of S(1),S(2),... are governed by a system of random recurrence equations. Such recurrence equations are of wide applied relevance and arise, among other places, in the study of GARCH financial models and insurance models with investments on the surplus capital. It will be shown that an asymptotic result very similar to (*) can also be developed in this setting.

• Prof. Dr. Freddy Delbaen (Department of Mathematics, ETH Zürich)
  Copherent risk measures in insurance
  
  Abstract: The idea of coherent risk measures can be used to define multiperiod coherent risk measures. The development leads to a recursive procedure. We will explain the ideas using a binomial model. The general case will be treated in the forthcoming papers on the subject. The co-authors in this work are Artzner, Eber, Heath and Ku.

• Prof. Dr. Freddy Delbaen (Department of Mathematics, ETH Zürich)
  Monotone selection in Poisson arrivals

• Dr. Henry Schellhorn
  A theory of combination trading and large scale systems for risk management

• Dr. Jörg Behrens (Andersen ZH)
  Credit risk in practice
  
  Abstract: Recent credit events and regulatory changes in capital treatment highlight the importance of proper credit risk management. For this talk, I have selected three practical examples to illustrate typical industry needs in this field: "The new Basel accord vs. standard portfolio models", "problems with exposure computation" and "the hassle with the computation of loss distributions".

• Dipl.-Ing. Dr. Hansjörg Albrecher (Department of Mathematics, Graz University of Technology, Austria)
  On some generalizations of the classical ruin model in risk theory
  
  Abstract: The classical model in collective risk theory for the development of the free reserve of an insurance portfolio is characterized by a Poisson claim number process, independent and identically distributed claims and a constant premium density. Several generalizations of this model are considered. In a ruin model allowing for a constant force of inflation and interest on the free reserve, we investigate when it is suitable to represent the finite-time survival probability as a gamma series and derive some exact analytical solutions for exponentially distributed claim sizes. In a model with dividend payments according to a non-linear dividend barrier strategy, integro-differential equations for the survival probability and the expected discounted dividend payments are derived and, using integral operators, efficient number-theoretic solution methods are developed. Moreover we investigate the behavior of the Lundberg exponent when dependence structures among consecutive claims are considered.

• Josef Teichmann (Department for Financial and Actuarial Mathematics, Vienna University of Technology)
  Existence of invariant manifolds for stochastic equations in infinite dimensions
  
  Abstract: We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimensions, in the spirit of Da Prato and Zabczyk. We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor. Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates. Analysis on Fréchet spaces will be explained with a review of different approaches and methods.

• Prof. Dr. Paul Embrechts (ETH Zürich)
  Integrated risk management for banking and insurance
  

• Prof. Dr. Eckhard Platen (University of Technology, Sydney)
  Perfect hedging of index derivatives
  
  Abstract: We present a financial market model that generates stochastic volatility using a minimal set of factors. These factors, formed from transformations of square root processes, model the dynamics of different denominations of a benchmark portfolio. Benchmarked prices are assumed to be local martingales. Numerical results for the pricing and hedging of basic derivatives on indices are described. This includes cases where the standard risk neutral pricing methodology fails. However, payoffs can be perfectly hedged using self-financing strategies and a form of arbitrage still exists. This is illustrated by hedge simulations. The term structure of implied volatilities is documented. (Joint work with David Heath, Sydney)

• Deimante Rusaityte (University of Copenhagen)
  Stability bounds for ruin probability
  
  Abstract: This talk is devoted to the stability problem of the ruin probability. We consider a rather general risk model which involves both Markov modulation and Lévy processes driven investments. Applying regenerative techniques we derive quantitative stability bounds for the probability of ruin. Let us emphasize the following features of the work. First, the model is more general than considered earlier by the Markov chain approach. Second, the stability bounds are stated in terms of the weighted uniform distance, and in this sense are more practical than the bounds obtained by the Markov chain approach which are stated in the weighted total variation distance.

Page created and supported by Uwe Schmock until September 2003. Last update: October 14, 2003