Date/Time : 04 Jul 2024 14:00
Venue : S16 #03-05/06
Speaker : Libo Li, University of New South Wales, Sydney

We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a non-zero probability. Similarly, the upper and lower prices for an vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a non-zero probability.

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Date/Time : 01 Dec 2023 15:00
Venue : S17 #04-06 (SR1)
Speaker : Min Dai, Hong Kong Polytechnic University

We develop a reinforcement learning method to learn an optimal trading strategy in the presence of transaction costs. Using a connection between singular control and a Dynkin game for portfolio choice with transaction costs, we learn the value function and optimal policy of an associated randomized Dynkin game, where a regularization term is incorporated to encourage exploration. We show that the policy efficiently approximates the optimal trading strategy. We design a reinforcement learning algorithm, which is demonstrated by numerical results. This work is jointly with Yuchao Dong.

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Date/Time : 21 Feb 2023 16:15
Venue : S17 #04-06 (SR1)
Speaker : Eliana Fausti, University of Oxford

Nonlinear filtering consists in finding the best estimate for the true value of a system when only incomplete, noisy observations are available. Since the filtering equations are often very high dimensional, and not tractable from a practical perspective, many applications must rely on approximation methods. Understanding the error of several such approximations remains an open problem. In this talk we will focus on the case where the underlying process is a continuous-time finite-state Markov chain. Leveraging tools from information geometry, we will show how to obtain a contraction result for the filtering equations, strengthening now-classical results on the stability of filters. This allows us to characterize the error of approximate filters, and to construct a low-dimensional geometric approximation with a well-behaved, hopefully small, error.  (Joint work with Sam Cohen, Oxford).

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