Руководитель: Кабанов Юрий Михайлович.
Колпаков Д.В. email@example.com
Время проведения: суббота 15:00.
Topic: «Fourier Based Methods for the Management of Complex Life Insurance Products».
Докладчик: Ernst Eberlein (University of Freiburg).
Аннотация: This paper proposes a framework for the valuation and the management of complex life insurance contracts, whose design can be described by a portfolio of embedded options, which are activated according to one or more triggering events. These events are in general monitored discretely over the life of the policy, due to the contract terms. Similar designs can also be found in other contexts, such as counterparty credit risk for example. The framework is based on Fourier transform methods as they allow to derive convenient closed analytical formulas for a broad spectrum of underlying dynamics. Multidimensionality issues generated by the discrete monitoring of the triggering events are dealt with efficiently designed Monte Carlo integration strategies. We illustrate the tractability of the proposed approach by means of a detailed study of ratchet variable annuities, which can be considered a prototypical example of these complex structured products.
Topic: «Bias-corrected Least Squares Monte Carlo for utility based optimal stochastic control problems».
Докладчик: Pavel V. Shevchenko (Actuarial Studies and Business Analytics, Macquarie University, Australia)
Аннотация: The Least-Squares Monte Carlo (LSMC) method has gained popularity in recent years due to its ability to handle multi-dimensional stochastic control problems, including problems with state variables affected by control. However, when applied to the stochastic control problems in the multi-period expected utility models, the regression fit tends to contain errors which accumulate over time and typically blow up the numerical solution. In this study we propose to transform the value function of the problems to improve the regression fit, and then using either the smearing estimate or smearing estimate with controlled heteroskedasticity to avoid the re-transformation bias in the estimates of the conditional expectations calculated in the LSMC algorithm. We also present and utilise recent improvements in the LSMC algorithms such as control randomisation with policy iteration to avoid accumulation of regression errors over time. Presented numerical examples demonstrate that transformation method leads to an accurate solution. In addition, in the forward simulation stage of the control randomisation algorithm, we propose a re-sampling of the state and control variables in their full domain at each time t and then simulating corresponding state variable at t+1, to improve the exploration of the state space that also appears to be critical to obtain a stable and accurate solution for the expected utility models.
Topic: «An Algorithmic Approach to Optimal Asset Liquidation Problems»
Докладчик: Juri Hinz (University of Technology Sydney)
Аннотация: Optimal control problems of stochastic switching type appear frequently in applications but are notoriously challenging from computational viewpoint. Furthermore, given a numerical approximation of the optimal control strategy, its quality is not easy to assess. Using duality techniques of by C. Rogers, we examine an efficient recursive algorithm which yields upper and lower bounds to perform diagnostics of numerical solutions to certain stochastic switching problems. We extend this approach to control problems under partial observability and illustrate our techniques by applications to mining operations and asset liquidation.
Topic: «On pricing rules and optimal strategies in general Kyle-Back models»
Докладчик: Albina Danilova (The London School of Economics)
Аннотация: The folk result in Kyle-Back models states that the value function of the insider remains unchanged when her admissible strategies are restricted to absolutely continuous ones. In this talk I will show that, for a large class of pricing rules used in current literature, the value function of the insider can be finite when her strategies are restricted to be absolutely continuous and infinite when this restriction is not imposed. This implies that the folk result doesn’t hold for those pricing rules and that they are not consistent with equilibrium. I will derive the necessary conditions for a pricing rule to be consistent with equilibrium and prove that, when a pricing rule satisfies these necessary conditions, the insider’s optimal strategy is absolutely continuous, thus obtaining the classical result in a more general setting.
This, furthermore, allows to justify the standard assumption of absolute continuity of insider’s strategies since one can construct a pricing rule satisfying the derived necessary conditions that yield the same price process as the pricing rules employed in the modern literature when insider’s strategies are absolutely continuous.
Topic: «Practical Aspects of Risk Based Margining»
Докладчик: Rostislav S. Protassov (Independent Consultant)
Аннотация: Risk assessment for a portfolio of diverse financial instruments can be a challenge. Under certain conditions, near term risk (short horizon, e.g., 10 business days) is quite amenable to a generic and extensible solution. For liquid portfolios, near term risk can serve as a basis for margin for a counterparty to collect (or post) against the portfolio, although regulation, if applicable, can introduce nuances. In this talk we shall discuss what features a robust and extensible portfolio-level risk assessment system should have, and how these features dictate its architecture. We shall also take a look at how regulation may introduce complexity to margining and, at times, discourage what should have otherwise been risk reducing activities.
Докладчики: Dmitry Muravey (Moscow State University) joined work with Andrey Itkin.
Topic: «Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit».
Abstract: This talk is devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, e.g., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems.
Докладчик: Miryana Grigorova (University of Leeds) https://www.miryanagrigorova.com.
Topic: «Pricing and hedging of options in a non-linear incomplete market model».
Abstract: We will review some well-known basic examples of complete and incomplete financial market models (in the linear case), in which we will illustrate the application of the so-called BSDE (the approach based on Backward Stochastic Differential Equations). We will then focus on some more involved financial models with possible default on the underlying risky asset, combined with different market “imperfections” leading to non-linear expectation operators. We will explain how the pricing and hedging problem of a European option in such market models leads to a stochastic control problem with non-linear expectations/ evaluations and to non-linear BSDEs with constraints.
If time permits, we will explain how the pricing and hedging problem of an American option in such models leads to a mixed stochastic control/stopping problem with non-linear expectations/ evaluations, and to non-linear Reflected BSDEs with constraints.
Докладчик: Marvin Mueller (Zurich).
Topic: «Statistical combination of analyst forecasts».
Abstract: Financial analysts investigate different companies and make estimates about the future performance of the stocks in terms of buy, hold or sell recommendations. In this talk, we discuss statistical learning methods to combine these recommendations of the analysts into a single trading signal using the analysts’ historical performance. Building upon recent work of Bew et al (2019) in this direction, we consider the problem from both frequentist and Bayesian machine learning perspective. We discuss the models, their numerical implementations, and the model performance based on a dataset of more than 3000 companies.
Докладчики: Эрнст Пресман (Москва, ЦЭМИ РАН), Isaac Sonin (Univerity of North Caroline in Charlotte).
Topic: «Модель управления запасами с ценами на сырьё, зависящими от цепи Маркова с непрерывным временем». Резюме:
Имеется производитель, которому нужно с постоянной интенсивностью потреблять сырьё. Цена на сырьё зависит от состояния марковской цепи с непрерывным временем. Целесообразно организовать склад и проводить как непрерывные, так и дискретные закупки товара. Затраты при хранении товара пропорциональны его количеству на складе.
Задача состоит в организации работы склада с целью минимизации дисконтированных или долговременных средних издержек на покупку и хранение. Оказывается, что в этой задаче оптимальное управление носит пороговый или квазипороговый характер. Для дисконтированных издержек приводится уравнение для производной от цены игры и алгоритм его решения, позволяющий находить оптимальные пороги и цену игры. Случай долговременного среднего получается предельным переходом при коэффициенте дисконтирования, стремящемся к нулю.
Докладчик: Александр Липтон (Массачусетский технологический институт, MIT).
Topic: «Blockchains in retrospective and perspective».
Denis Belomestny (University of Duisburg-Essen)
Topic: “Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm” https://disk.yandex.ru/i/5ztbShoaJK24Cg.
Abstract: In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete-time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by −4 log +2(1∕ ) with being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous- time optimal stopping problems and derive the correspond-ing complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example.
Михаил Урусов из университета Дуйсбурга-Эссена.
Topic: Trade execution with stochastic liquidity in discrete and continuous time.
Abstract: We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end, we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions. In discrete time, we discuss an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs and observes some qualitative differences with related models. In continuous time, due to the stochastic dynamics of the order book depth and resilience, optimal execution strategies are typically of infinite variation, and the first thing to be discussed it how to extend the state dynamics and the cost functional to allow for general semimartingale strategies. We then derive a quadratic BSDE that under appropriate assumptions characterizes minimal execution costs, identifies conditions under which an optimal execution strategy exists and, finally, illustrates our findings in several examples. This is a joint work with Julia Ackermann and Thomas Kruse.
13.02.2021 в 11:00 мск.
Prof Kostya Borovkov (Univeristy of Melbourne).
Topic: The exact asymptotics of the large deviation probabilities in the multivariate boundary crossing problem.
Abstract: For a multivariate random walk with i.i.d. jumps satisfying the Cramér moment condition and having mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by and extends results from a paper by F. Avram et al. (2008) on a two-dimensional risk process. Our approach combines the large deviation techniques from a series of papers by A. Borovkov and A. Mogulskii from around 2000 with new auxiliary constructions, which enable us to extend their results on hitting remote sets with smooth boundaries to the case of boundaries with a “corner” at the “most probable hitting point”. We also discuss how our results can be extended to the case of more general target sets. Joint work with Yuqing Pan.
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