Руководитель: Кабанов Юрий Михайлович.
Колпаков Д.В. firstname.lastname@example.org
Время проведения: суббота 15:00.
Alexander Melnikov (University of Alberta, Edmonton, AB, CANADA)
Topic: On Modifications of the Bachelier model and Option Pricing
Abstract: In the talk we consider some aspects of financial market modeling as well as option pricing. Our main goal is to provide a new look at the classical Bachelier model. We transform it to make stock prices non-negative. The most well-known transformation is exponential one which leads to the geometric Brownian motion or the Black-Scholes model. We develop here another method of getting such modifications which is based on SDEs with absorption and reflection. In the framework of these modifications we also discuss problems of perfect and imperfect hedging. Formulas of quantile and CVaR-hedging will be derived. Moreover, it will be shown how these results are applied in the areas of regulatory capital and life insurance.
Pergamenshchikov S.M. (CNRS-Université de Rouen, France)
Topic: Hedging problems for Asian options with transaction costs
Abstract: In this talk we develop asymptotic Asian option hedging methods for the Black – Scholes markets with transaction costs. Firstly, we construct the classical replication strategies and then, using the Leland approach, we propose the corresponding modifications for the financial markets with proportional transaction costs. We find sufficient conditions on the transaction costs under which we provide the asymptotic hedging for the constructed strategies. Then, we consider the pricing problem as well. We study three cases: the option price is the same as for the hedging problem without transaction costs, the increasing volatility case and the case when the option price equals to the option price of the “buy and hold” strategy.
Juri Hinz (University of Technology Sydney)
Topic: On optimal planning of double-spending attacks.
Abstract: Diverse concepts originating from the blockchain idea have gained popularity. However, there is concern about stability of such systems. In this setting, an attempt to spend the digital funds more than once (the so-called double-spending attack) has been analyzed by several authors.The present contribution addresses a refinement to this problem under realistic assumptions.
Topic: Towards geometry and set-valued functions in multivariate finance
Ilya Molchanov (Bern)
Abstract: When dealing with several assets, it is usually possible to combine or exchange them in many ways. Accordingly, the family of admissible portfolios is a (usually convex) set in the Euclidean space. The talk explains the relevant basic mathematical constructions and then concentrates on the analogues of the concepts of convexity and concavity. Their relevance in assessing risks of mutiasset portfolios will be particularly emphasised.
Peter Tankov (ENSAE, Paris)
Topic: Price formation and optimal trading in intraday electricity markets
Abstract: We develop a tractable equilibrium model for price formation in intraday electricity markets in the presence of intermittent renewable generation. Using stochastic control theory we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form for a finite number of agents as well as in the asymptotic framework of mean field games. We consider both the setting of homogeneous agents and the one where a major producer may interact strategically with a large number of small producers. Our model reproduces the empirical features of intraday market prices, such as increasing price volatility at the approach of the delivery date and the correlation between price and renewable infeed forecasts, and relates these features with market characteristics like liquidity, number of agents, and imbalance penalty.
Дмитрий Крамков (профессор Университета Карнеги-Меллон)
Topic: An optimal transport problem with backward martingale constraints motivated by insider trading