Talks in Financial and Insurance Mathematics

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This is the regular weekly research seminar on Insurance Mathematics and Stochastic Finance.

Autumn Semester 2014

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
28 August 2014
Prof. Dr. Sergey Nadtochiy 
University of Michigan
Robust Hedging of Barrier Options with Beliefs on Implied Volatility  HG G 43 
Abstract: In this talk, I will demonstrate the method of robust pricing and hedging with beliefs, by considering the problem of hedging a barrier option with the European options and the underlying. This setting includes continuous time and beliefs on the possible future values of implied volatilities. In general, the beliefs can be understood as a set of possible paths for the prices of all liquid instruments. They are meant to be constructed using prior observations: e.g. the upper and lower bounds on the future values of implied volatilities can be obtained from the historical option prices. I will start with a duality result which relates the super-hedging price of a barrier option to the expectations under martingale measures. This result connects the super-hedging price, defined path-wise, with no a priori given probability measures, to the classical probabilistic models. However, its applications are limited by the fact that, typically, the associated optimal super-hedging strategies are not computation- ally tractable. Therefore, the second part of my talk focuses on the super-hedging strategies that can be constructed explicitly. I will show how to construct such strategies in the case when the beliefs on implied volatilities admit a so-called extremal model. The resulting super-hedging strategy may or may not be optimal, depending on whether the initial combination of options prices agrees with the extremal model. Nevertheless, I will show that such strategies possess the asymptotic optimality properties. I will illustrate the theoretical results with numerical examples, using the real-world data.
2 October 2014
Dr. Umut Cetin
London School of Economics
Competition among risk averse market makers and inverse problems  HG G 43 
Abstract: We discuss the impact of risk aversion of market makers on the equilibrium price in a Kyle model. The talk will consist of two parts. The first part will focus on the case when the informed trader has a static signal and illustrate the deviations form the standard Kyle model as a result of risk aversion by analysing various liquidity measures such as depth, resiliency and price reversal. When the informed trader receives a continuous signal changing over time, the existence of an equilibrium becomes a delicate issue. We will see that the question of existence is related to an ill-posed inverse problem for a backward parabolic equation with a given initial condition. We will discuss some necessary and sufficient conditions in order for the inverse problem to have a solution along with their interpretations in terms of Bessel processes.
16 October 2014
Dr. Andrea Macrina
Randomised Markov Bridges  HG G 43 
Abstract: We consider the filtering problem of estimating a hidden random variable X by noisy observations. The noisy observation process is constructed by a randomised Markov bridge (RMB) {Zt}0 ≤ t ≤ T of which terminal value is set to ZT = X. That is, at the terminal time T, the noise of the bridge process vanishes and the hidden random variable X is revealed. We derive the explicit filtering formula, also called the Bayesian posterior probability formula, for a general RMB. It turns out that the posterior probability is given by a function of the current time t, the current observation {Zt}, the initial observation {Z0}, and the prior distribution ν of X. (Joint work with Jun Sekine, Osaka University.)
23 October 2014
Marvin Müller
TU Berlin
Stochastic Moving Boundary Problems and Limit Order Book Models  HG G 43 
Abstract: We introduce a class of continuous models for the limit order book density with infinitesimal tick size, where the evolution of buy and sell side is described by a semilinear second-order SPDE and the mid price process defines a free boundary separating buy and sell side. Price changes are assumed to be determined by the bid-ask imbalance. The resulting limit order book model can be considered as a generalization of the linear stochastic Stefan problem introduced by Kim, Sowers and Zheng (2012). In order to show existence of a solution we transform the problem into a stochastic evolution equation, where the boundary interaction leads to an additional drift. Regularity properties of the linear part in the equation allow to control the non-linearities and establish (local) existence and uniqueness results. This provides a framework for further analysis of the problem, including Wong-Zakai type approximations and positivity of the order volume in the model.
30 October 2014
Dr. Miklós Rásonyi
Pázmány Péter Catholic University, Faculty of Information Technology and Bionics
Optimal investment beyond expected utility theory  HG G 43 
Abstract: I will discuss some recent results on optimal investment in incomplete markets under preferences involving probability distortions, such as those of cumulative prospect theory. Part of the mathematical difficulties is related to the closedness of the set of attainable portfolio values for convergence in law. I will present a counterexample and then positive results both in discrete and in continuous time.
6 November 2014
Dr. Remy Praz
Copenhagen Business School
Asymmetric Information and Inventory Concerns in Over-the-Counter Markets  HG G 43 
Abstract: We study how transparency affects the functioning of an over-the-counter market by introducing asymmetric information about investors' liquidity needs within a search-and-matching model. Transparency improves the allocative efficiency of the market, but makes inventories costly: it both induces opportunistic liquidity provision and reduces the number of counterparties willing to absorb large liquidity demands. When deciding whether or not to participate in the market, an investor must balance increased efficiency against increased inventory costs, leading to an ambiguous relation between transparency and market participation. The equilibrium is fragile---a marginal increase in transparency can trigger abrupt liquidity and welfare drops. (Joint work with Julien Cujean from Robert H. Smith School of Business, University of Maryland)
13 November 2014
Dr. Paul Krühner
Technische Universität Dortmund
On finite dimensional approximation of infinite dimensional forward price models  HG G 43 
Abstract: The Heath-Jarrow-Morton type approach treats a family of securities — written on an underlying — as primary assets and models them directly. Originally, this reasonable approach has been used for the modelling of bond prices. We adopt this approach for modelling in electricity markets and model a curve valued process which has a straightforward relation to the prices of forwards with delivery periods. These forwards are the mainly traded securities in electricity markets. In this talk, we present a formula for the dynamics of the resulting forwards in a non-Gaussian setting and we present an approximation theorem for the forward prices with arbitrage free models which have a finite dimensional state space and affine-like dynamics.
20 November 2014
Dr. Nicolas Perkowski
Université Paris Dauphine
Unbounded profits in classical and model free financial mathematics  HG G 43 
Abstract: We will discuss the notion of “no unbounded profit with bounded risk” and some of its implications for asset price models. I will also present a model free formulation of it and show how it can be used to construct a model free Ito integral and to derive path properties of typical asset price trajectories. Based on joint works with Peter Imkeller, David Prömel, and Johannes Ruf.
27 November 2014
Prof. Dr. Eva Lütkebohmert-Holtz
University of Freiburg
Funding Liquidity, Debt Tenor Structure, and Creditor's Belief: An Exogenous Dynamic Debt Run Model  HG G 43 
Abstract: We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollover dates of short-term debt, creditors face a dynamic coordination problem. We show that a unique threshold strategy (i.e., a debt run barrier) exists for short-term creditors to decide when to withdraw their funding, and this strategy is closely related to the solution of a non-standard optimal stopping time problem with control constraints. We decompose the total credit risk into an insolvency component and an illiquidity component based on such an endogenous debt run barrier together with an exogenous insolvency barrier. (Joint work with Gechun Liang und Wei Wei.)

Organizers: Paul Embrechts , Martin Schweizer , Halil Mete Soner , Josef Teichmann , Mario Valentin Wüthrich 

Archive: 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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