One World Optimal Stopping and Related Topics

Online seminars

This is an international online seminar where recent work on optimal stopping theory and related topics is presented. The seminar is a part of One World Seminars that were inspired by One World Probability project.

Organizers:

Tiziano De Angelis (University of Turin)

Roxana Dumitrescu (King's College)

Yerkin Kitapbayev (North Carolina State University)

Mikhail Zhitlukhin (Steklov Mathematical Institute)

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Schedule for Fall 2021

Sep 22, 2021, 5 pm London time

Damien Lamberton, Université Gustave Eiffel

Title: On the American put in the Heston model

Abstract: We study some qualitative properties of the American put price in the Heston model. In particular, we will discuss the monotonicity with respect to volatility, regularity properties, strict convexity in the continuation region. [This talk is based on joint work with Giulia Terenzi.]

Oct 6, 2021, 5 pm London time

Emma Hubert, Princeton University

Title: Epidemic control: individual and governmental perspective


Abstract: In this talk, we consider the control of the COVID-19 pandemic from two point of views: individual and governmental. In the first part, through a standard SIR compartmental model, we assume that the control is induced by the aggregation of individuals’ decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralised decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. This lead us to consider, in the second part, the governmental point of view. In this model, the population is considered as a single agent, but the government can put into place incentive policies to encourage the lockdown. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. Numerical results confirm the relevance of a tax and testing policy to improve the control of an epidemic. [Joint works with Romuald Elie, Thibaut Mastrolia, Dylan Possamaï, Gabriel Turinici and Xavier Warin.]

Oct 20, 2021, 5 pm London time

Zbigniew Palmowski, Wrocław University of Science and Technology

Title: Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functions


Abstract: In this talk we analyse some equity-linked contracts that are related to drawdown and drawup events based on assets governed by a geometric spectrally negative Lévy process. Drawdown and drawup refer to the differences between the historical maximum and minimum of the asset price and its current value, respectively. We consider four contracts. In the first contract, a protection buyer pays a premium with a constant intensity p until the drawdown of fixed size occurs. In return, he/she receives a certain insured amount at the drawdown epoch, which depends on the drawdown level at that moment. Next, the insurance contract may expire earlier if a certain fixed drawup event occurs prior to the fixed drawdown. The last two contracts are extensions of the previous ones but with an additional cancellable feature that allows the investor to terminate the contracts earlier. In these cases, a fee for early stopping depends on the drawdown level at the stopping epoch. In this work, we focus on two problems: calculating the fair premium p for basic contracts and finding the optimal stopping rule for the polices with a cancellable feature. To do this, we use a fluctuation theory of Lévy processes and rely on a theory of optimal stopping. [The talk is based on a joint work with J. Tumilewicz.]


Nov 3, 2021, 5 pm London time

Huyen Pham, Paris Diderot

Title: Optimal bidding strategies for digital advertising

Abstract: With the emergence of new online channels and information technology, digital advertising plays a growing role in our society and tends to substitute more and more to traditional advertising (like newpapers, TV, billboards). Indeed, companies can minimize their ad costs by targeting directly users/individuals that are potentially interested by their products. We develop several models of targeted advertising with auctions. Each model focuses on a different type of advertising, namely, commercial advertising for triggering purchases or subscriptions, and social marketing for sensitizing people about unhealthy behaviors (anti-drug, road-safety campaigns). All our models are based on a common framework encoding people's online behaviours and the targeted advertising auction mechanism widely used on Internet. Our main results are to provide semi-explicit formulas for the optimal value and bidding policy for each of these problems. By means of these formulas, we are able to analyze and interpret how phenomenons like people's online behaviors and social interactions affect the optimal bid for targeted advertising auctions. We also study how to efficiently combine targeted advertising and non-targeted advertising mechanism. We conclude by providing some classes of examples with fully explicit formulas. [Based on joint work with Médéric Motte (Université de Paris).]

Nov 17, 2021, 12 pm London time (Postponed until Spring 2022)

Anna Aksamit, The University of Sydney


Dec 8, 2021, 5 pm London time

Yu-Jui Huang, University of Colorado Boulder

Title: A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria

Abstract: This talk focuses on a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve time inconsistency triggered by non-exponential discounting. Next, given the other player's chosen stopping policy, each player selects a best response among her intra-personal equilibria. A resulting inter-personal equilibrium is then a Nash equilibrium between the two players, each of whom employs her best intra-personal equilibrium with respect to the other player's stopping policy. Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorn's lemma. To illustrate our theoretic results, we investigate a two-player real options valuation problem: two firms negotiate a deal of cooperation to initiate a project jointly. By deriving inter-personal equilibria explicitly, we find that coercive power in negotiation depends crucially on the impatience levels of the two firms.

Dec 15, 2021, 5 pm London time

Peter Carr, NYU

Title: Stoptions: Representations and Applications

Abstract: TBA.