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Spring Semester 2012

Date / Time Speaker Title Location
2 February 2012
17:15-18:15 		Prof. Dr. Nizar Touzi
Ecole Polytechnique
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Talks in Financial and Insurance Mathematics

Title Maximum maximum of martingales given finitely many intermediate marginals
Speaker, Affiliation Prof. Dr. Nizar Touzi, Ecole Polytechnique
Date, Time 2 February 2012, 17:15-18:15
Location HG G 43
Abstract Following our previous work, we consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes and finitely-many maturities. The dual formulation converts this problem into a continuous martingale optimal transportation problem which we solve explicitly for Lookback options with nondecreasing payoff function. In particular, our methodology recovers the extensions of the Azema-Yor solution of the Skorohod embedding problem obtained by Hobson and Klimmek (under slightly stronger conditions), those derived by Brown, Hobson and Rogers, and those obtained by Madan and Yor.
Maximum maximum of martingales given finitely many intermediate marginalsread_more
HG G 43
9 February 2012
17:15-18:15 		Mykhaylo Shkolnikov
Stanford University
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Talks in Financial and Insurance Mathematics

Title On diffusions interacting through their ranks
Speaker, Affiliation Mykhaylo Shkolnikov, Stanford University
Date, Time 9 February 2012, 17:15-18:15
Location HG G 43
Abstract We will discuss systems of diffusion processes on the real line, in which the dynamics of every single process is determined by its rank in the entire particle system. Such systems arise in mathematical finance and statistical physics, and are related to heavy-traffic approximations of queueing networks. Motivated by the applications, we address questions about invariant distributions, convergence to equilibrium and concentration of measure for certain statistics, as well as hydrodynamic limits and large deviations for these particle systems. Parts of the talk are joint works with Amir Dembo, Tomoyuki Ichiba, Soumik Pal and Ofer Zeitouni.
On diffusions interacting through their ranksread_more
HG G 43
23 February 2012
17:15-18:15 		Prof. Dr. Mikhail Urusov
University of Ulm, Germany
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Talks in Financial and Insurance Mathematics

Title Deterministic Criteria for the Absence of Arbitrage in one-Dimensional Diffusion Models
Speaker, Affiliation Prof. Dr. Mikhail Urusov, University of Ulm, Germany
Date, Time 23 February 2012, 17:15-18:15
Location HG G 43
Abstract We present deterministic necessary and sufficient conditions for no free lunch with vanishing risk (NFLVR), no generalized arbitrage (NGA) and no relative arbitrage (NRA) in one-dimensional diffusion models and examine relations between these no-arbitrage notions. In particular, it turns out that NFLVR and NRA neither imply nor exclude each other, while NGA is equivalent to NFLVR and NRA. This is a joint work with Aleksandar Mijatović.
Deterministic Criteria for the Absence of Arbitrage in one-Dimensional Diffusion Modelsread_more
HG G 43
* 1 March 2012
16:00-17:00 		Prof. Dr. Giovanni Puccetti
University of Firenze
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Talks in Financial and Insurance Mathematics

Title Sharp bounds for sums of dependent risks
Speaker, Affiliation Prof. Dr. Giovanni Puccetti, University of Firenze
Date, Time 1 March 2012, 16:00-17:00
Location HG D 3.1
Abstract Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure are known from Makarov(1981) and Rüschendorf(1982) for d=2 and, in some examples, for d>=3. For identically distributed random variables, Embrechts and Puccetti(2006) introduced a class of dual bounds for this problem for d>=3 based on mass transportations. In this talk we give a proof of the sharpness of these dual bounds. Joint work with L. Rüschendorf.
Sharp bounds for sums of dependent risksread_more
HG D 3.1
8 March 2012
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Title No Talk Scheduled
Speaker, Affiliation
Date, Time 8 March 2012, 17:15-18:15
Location
No Talk Scheduled
15 March 2012
17:15-18:15 		Prof. Dr. Marcel Nutz
Columbia University
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Talks in Financial and Insurance Mathematics

Title G-Expectation for General Random Variables
Speaker, Affiliation Prof. Dr. Marcel Nutz, Columbia University
Date, Time 15 March 2012, 17:15-18:15
Location HG G 43
Abstract We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. In particular, we construct the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable.
G-Expectation for General Random Variablesread_more
HG G 43
22 March 2012
17:15-18:15 		Prof. Dr. Henrik Shahgholian
The Royal Institute of Technology of Sweden
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Talks in Financial and Insurance Mathematics

Title Problems in mathematical finance with free boundaries
Speaker, Affiliation Prof. Dr. Henrik Shahgholian, The Royal Institute of Technology of Sweden
Date, Time 22 March 2012, 17:15-18:15
Location HG G 43
Abstract I shall discuss certain techniques in free boundaries related to American type contracts. Such techniques are of general nature and have the advantage of being applied to general framework in applications. Our focus shall be on the behavior of the solution function as well as the free boundary, close to initial state (American Option) or close to Dirichlet data (Convertible Bonds).
Problems in mathematical finance with free boundariesread_more
HG G 43
29 March 2012
17:15-18:15
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Talks in Financial and Insurance Mathematics

Title No Talk Scheduled
Speaker, Affiliation
Date, Time 29 March 2012, 17:15-18:15
Location
No Talk Scheduled
* 4 April 2012
15:30-16:30 		Jin-Hyuk Choi
University of Texas Austin
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Talks in Financial and Insurance Mathematics

Title Shadow prices and well posedness in the problem of optimal investment and consumption with transaction costs
Speaker, Affiliation Jin-Hyuk Choi, University of Texas Austin
Date, Time 4 April 2012, 15:30-16:30
Location HG G 19.1
Abstract We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the HJB equation for this singular stochastic control problem to a free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a twicely differenciable solution, we use it to construct the solution of the original optimal investment/consumption problem without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.
Shadow prices and well posedness in the problem of optimal investment and consumption with transaction costsread_more
HG G 19.1
5 April 2012
17:15-18:15
Details

Talks in Financial and Insurance Mathematics

Title No Talk (ETH Closes Early)
Speaker, Affiliation
Date, Time 5 April 2012, 17:15-18:15
Location
No Talk (ETH Closes Early)
19 April 2012
17:15-18:15 		Prof. Dr. Paul Embrechts
ETH Zürich
Details

Talks in Financial and Insurance Mathematics

Title Abel, Tauber, Mercer, Karamata, Regular Variation and Subexponential Distributions
Speaker, Affiliation Prof. Dr. Paul Embrechts, ETH Zürich
Date, Time 19 April 2012, 17:15-18:15
Location HG G 43
Abstract The aim of this talk is to show how the various parts of the title belong together. The mathematical excursion will take us from classical Tauberian theory to the modelling of extremal events. Included is an application to actuarial ruin theory and the asymptotic behaviour of infinitely divisible distributions. I end with an open problem from the realm of renewal theory.
Abel, Tauber, Mercer, Karamata, Regular Variation and Subexponential Distributionsread_more
HG G 43
26 April 2012
17:15-18:15 		Prof. Dr. Christian Bayer
WIAS, Deutschland
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Talks in Financial and Insurance Mathematics

Title Some applications of the Ninomiya-Victoir scheme in the context of financial engineering
Speaker, Affiliation Prof. Dr. Christian Bayer, WIAS, Deutschland
Date, Time 26 April 2012, 17:15-18:15
Location HG G 43
Abstract Based on ideas from rough path analysis and operator splitting, the Kusuoka-Lyons-Victoir scheme provides a familiy of higher order methods for the weak approximation of stochastic differential equations. Out of this family, the Ninomiya-Victoir method is especially simple to implement and to adjust to various different models. We give some examples of models used in financial engineering and comment on the performance of the Ninomiya-Victoir scheme and some modifications when applied to these models.
Some applications of the Ninomiya-Victoir scheme in the context of financial engineeringread_more
HG G 43
3 May 2012
17:15-18:15 		Dr. Mathias Beiglböck
Universität Wien
Details

Talks in Financial and Insurance Mathematics

Title Mass Transport, Robust Pricing and Trajectorial Inequalities
Speaker, Affiliation Dr. Mathias Beiglböck, Universität Wien
Date, Time 3 May 2012, 17:15-18:15
Location HG G 43
Abstract Robust pricing of an exotic option with payoff Phi can be viewed as the task of estimating E_Q Phi, where Q runs through a set of martingale measures satisfying marginal constraints. It is fruitful to relate this to the theory of mass transportation. E.g. the abstract duality theorem from optimal transport leads to new superreplication results. This dual viewpoint also provides new insights on classical martingale inequalities.
Mass Transport, Robust Pricing and Trajectorial Inequalitiesread_more
HG G 43
* 9 May 2012
15:15-16:15 		Prof. Dr. Miklos Rasonyi
University of Edinburgh
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Talks in Financial and Insurance Mathematics

Title Optimal investment: from risk-averse to behavioural agents
Speaker, Affiliation Prof. Dr. Miklos Rasonyi, University of Edinburgh
Date, Time 9 May 2012, 15:15-16:15
Location HG G 19.1
Abstract Classical investment problems assume that economic agents are risk-averse. This corresponds to using concave utility functions to describe agents' preferences. More recently, non-concave utilities were proposed and distortions of the probability measure were also considered. We are dealing with optimal investment for an agent whose behaviour is characterized by a possibly non-concave utility function and by probability distortions. This new setting poses several mathematical challenges and exhibits a number of unexpected phenomena. In discrete-time multiperiod models we discuss the well-posedness of this investment problem and show the existence of optimal strategies under suitable conditions. We also have a look at what happens in continuous-time, in particular, we provide a sufficient and (essentially) necessary condition for the Black-Scholes model in the case of power-like utilities and distortion functions.
Optimal investment: from risk-averse to behavioural agentsread_more
HG G 19.1
10 May 2012
17:15-18:15 		Erhan Bayraktar
University of Michigan
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Talks in Financial and Insurance Mathematics

Title Stochastic Perron's method and verification without smoothness using viscosity comparison
Speaker, Affiliation Erhan Bayraktar, University of Michigan
Date, Time 10 May 2012, 17:15-18:15
Location HG G 43
Abstract We adapt the Stochastic Perron's method in Bayraktar and Sirbu (ArXiv: 1103.0538) to the case of double obstacle problems associated to Dynkin games. We construct, symmetrically, a viscosity sub-solution which dominates the upper value of the game and a viscosity super-solution lying below the lower value of the game. If the double obstacle problem satisfies the viscosity comparison property, then the game has a value which is equal to the unique and continuous viscosity solution. In addition, the optimal strategies of the two players are equal to the first hitting times of the two stopping regions, as expected. The (single) obstacle problem associated to optimal stopping can be viewed as a very particular case. This is the first instance of a non-linear problem where the Stochastic Perron's method can be applied successfully.
Stochastic Perron's method and verification without smoothness using viscosity comparisonread_more
HG G 43
17 May 2012
00:00-23:59
Details

Talks in Financial and Insurance Mathematics

Title No Talk (ETH Closed)
Speaker, Affiliation
Date, Time 17 May 2012, 00:00-23:59
Location
No Talk (ETH Closed)
* 18 May 2012
14:00-15:00 		Prof. Dr. Peter Bank
TU Berlin
Details

Talks in Financial and Insurance Mathematics

Title Optimal Order Placement
Speaker, Affiliation Prof. Dr. Peter Bank, TU Berlin
Date, Time 18 May 2012, 14:00-15:00
Location HG G 19.1
Abstract The execution of large transactions on a financial market will typically affect market prices in an adverse manner, thus leading to possibly significant execution costs. Minimizing these costs requires to trade-off projections of future market depth vs. market resilience and vs. the urgency to trade. We present an extension of the model proposed by Obizhaeva and Wang which allows for these key market parameters to change over time and we show how to produce a closed-form solution to the resulting optimal control problem. (This is joint work with Antje Fruth.)
Optimal Order Placementread_more
HG G 19.1
24 May 2012
17:15-18:15 		Prof. Dr. Xunyu Zhou
University of Oxford
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Talks in Financial and Insurance Mathematics

Title Arrow-Debreu Equilibria for Rank-Dependent Utilities
Speaker, Affiliation Prof. Dr. Xunyu Zhou, University of Oxford
Date, Time 24 May 2012, 17:15-18:15
Location HG G 43
Abstract We provide conditions on a single period, two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we derive the state-price density explicitly, which is a weighted marginal rate of substitution between initial and end-of-period consumption of a representative agent, while the weight is expressed through the differential of the probability weighting function. A key step in our derivation is to obtain an analytical solution to the individual consumption problem that involves the concave envelope of certain non-concave function. Our results indicate that, under a "weighting-neutral probability" that is an appropriate modification of the original probability measure, assets can be priced in the same way as in an economy with expected utility agents.
Arrow-Debreu Equilibria for Rank-Dependent Utilitiesread_more (CANCELLED)
HG G 43
31 May 2012
17:15-18:15 		Prof. Dr. Dirk Becherer
Humboldt Universität Berlin
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Talks in Financial and Insurance Mathematics

Title On backward stochastic differential equations with jumps of infinite activity
Speaker, Affiliation Prof. Dr. Dirk Becherer, Humboldt Universität Berlin
Date, Time 31 May 2012, 17:15-18:15
Location HG G 43
Abstract We discuss backward stochastic differential equations driven jointly by a Brownian motion and a random measure. The random measure may be of infinite activity, for instance arrising as the jump measure of a Levy process like the Gamma process with infinitely many jumps in finite time. Assuming a structural form of the generator for the BSDE that separates dependence on the two stochastic integrands and imposes some form of monotonicity in the jump component but no global Lipschitz assumptions, we show existence and uniqueness of bounded solutions for the BSDE. Those can be applied to derive optimal investment strategies for utility maximization problems. (Joint work with Martin Büttner, HU Berlin)
On backward stochastic differential equations with jumps of infinite activityread_more
HG G 43
* 7 June 2012
17:15-18:15 		Prof. Dr. Suresh Sethi
University of Texas at Dallas
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Talks in Financial and Insurance Mathematics

Title Co-op Advertising and Pricing in a Stochastic Supply Chain: Feedback Stackelberg Strategies
Speaker, Affiliation Prof. Dr. Suresh Sethi, University of Texas at Dallas
Date, Time 7 June 2012, 17:15-18:15
Location HG G 19.1
Abstract Cooperative (co-op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co-op advertising policy, i.e., a participation or subsidy rate that specifies the percentage of the retailer’s advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi’s stochastic sales-advertising model of 1983. We obtain the condition under which offering co-op advertising is optimal for the manufacturer. We provide, in feedback form, the optimal advertising and pricing policies for the manufacturer and the retailer. We extend the analysis to a (deterministic) case of two retailers competing with one another, and solve the resulting Stackelberg-Nash differential game, in which the manufacturer announces his subsidy rates for the two retailers, and the retailers in response play a Nash differential game in choosing their optimal advertising efforts over time. We identify the key drivers that influence the optimal subsidy rates and obtain the conditions under which the manufacturer will support one or both of the retailers. We analyze the impact of co-op advertising on the profits of the channel members and the extent to which it can coordinate the channel. We investigate the case of an anti-discriminatory act which restricts the manufacturer to offering equal subsidy rates to the two retailers.
Co-op Advertising and Pricing in a Stochastic Supply Chain: Feedback Stackelberg Strategiesread_more
HG G 19.1
* 3 July 2012
17:00-18:00 		Prof. Dr. Paul Feehan
Rutgers State University of New Jersey
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Talks in Financial and Insurance Mathematics

Title C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical finance
Speaker, Affiliation Prof. Dr. Paul Feehan, Rutgers State University of New Jersey
Date, Time 3 July 2012, 17:00-18:00
Location HG G 43
Abstract The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted H\"older spaces, we establish the optimal C^{1,1} regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth. This is joint work with Panagiota Daskalopoulos.
C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical financeread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: Winslow Strong

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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