Date/Time : 30 Jan 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Philippe Codognet, Sorbonne University

Introduced in 1965 by John P. Costas for SONAR and RADAR applications, the notion of Costas Arrays, i.e., 2-dimension arrays with optimal autocorrelation properties, is a hard combinatorial problem with many applications.
Although several methods have been designed for constructing Costas Arrays, e.g. Golomb or Welch methods, there is no general method to construct all Costas Arrays for any given size n, which is an NP-complete problem, and thus one has to resort to exhaustive search for finding all Costas Arrays of size n.

All Costas Arrays up to size 29 have been discovered, some for size 30 and 31, but the existence of a Costas Array of size 32 is still an open problem after more than 60 years. This makes the Costas Array Problem (CAP) an interesting challenge for quantum computing, in particular for quantum optimization, which is the modeling and solving of combinatorial problems with quantum computations. In this domain, Quadratic Unconstrained Binary Optimization (QUBO) has emerged as a common paradigm for modeling and solving combinatorial problems either by quantum annealing (e.g. with the D-Wave quantum computers) or by the Quantum Optimization Approximation Algorithm (QAOA, on gate-based quantum architectures).

We will present in this talk a new QUBO model for the CAP aimed at an implementation on quantum computers. A few years ago, a direct modeling of the CAP with Boolean variables has been proposed, which requires O(n^4) QUBO variables for a CAP instance of size n, that is, n^4 logical qubits on a quantum computer, but further reduction is indeed possible. We thus propose a new model which requires only O(n^3) variables for a CAP instance of size n, making thus medium-size instances tractable on current quantum annealing hardware, e.g. D-Wave Advantage systems. This new model consider the (usual) representation the CAP as an integer-based Constrained Optimization Problem, where the Costas Array is represented as a permutation of {1, . . . , n} and focuses on the property that if the so-called “difference table” constructed from a permutation p do not have any repeated value for any line, then p represents a Costas Array. This property of the difference table can be enforced in the QUBO model by defining adequate penalty expressions corresponding to the at-most-one constraints (one for each line of the difference table). These penalty expressions are then added to the objective function as well as the penalty expression corresponding to the overall constraint to be a permutation.

We will moreover present implementation results for this new model and a comparison with the previous direct model, on D-Wave quantum annealer and on the quantum-inspired Fixstars Amplify Annealing Engine.

This seminar is a joint event between CQF and NUS Integrated Quantum & AI Computing Consortium.

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Date/Time : 23 Jan 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Qiang Liu, Shanghai University of Finance and Economics

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the high-frequency increments to deal with the effect of jumps, based on which the estimators of leverage effect and volatility of volatility are proposed. Compared with existing estimators, our method is valid under more general jumps, making it a better alternative for empirical applications. Under some mild conditions, the asymptotic normality of the estimators is established and consistent estimators of the limiting variances are proposed based on the estimation of volatility functionals. We conduct extensive simulation study to verify the theoretical results. The results demonstrate that our estimators have better performance than the existing ones, especially when the jump is of infinite variation. Besides, we apply our estimators to a real high-frequency dataset, which reveals nonzero leverage effect and volatility of volatility in the market. 

Register here: https://forms.office.com/r/Pa3vvSfTLu

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Date/Time : 22 Aug 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Marcel Nutz, Columbia University

Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection, which static trading fees often fail to offset in practice. We study the key determinants of LP profitability in a dynamic reduced-form model where an AMM operates in parallel with a centralized exchange (CEX), traders route their orders optimally to the venue offering the better price, and arbitrageurs exploit price discrepancies. Using large-scale simulations and real market data, we analyze how LP profits vary with market conditions such as volatility and trading volume, and characterize the optimal AMM fee as a function of these conditions. The mechanisms driving these relationships are highlighted through extensive comparative statics, and the model’s relevance is confirmed through calibration to market data. We find that under normal market conditions, the optimal AMM fee is competitive with the trading cost on the CEX and remarkably stable, whereas in periods of very high volatility, a high fee protects passive LPs from severe losses. These findings suggest a threshold-type dynamic fee schedule to improve LP outcomes. (Joint work with Steven Campbell, Philippe Bergault, Jason Milionis.)

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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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