Publications: Actuarial Science & Mathematical Finance

Algorithmic Trading, Stochastic Control, and Mutually Exciting Processes

by Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci

SIAM Review | 2018 | Issue: 60(3), 673–703

Short Summary: On electronic exchanges, orders tend to induce cross-excitation in market activity, e.g., when a buy order arrives it may induce increased activity of both buy and sell orders and induce changes in the limit order book. This paper develops a detailed model of this phonomena, and takes a mathematical look at the resulting optimal control problem.

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An IBNR-RBNS insurance risk model with marked Poisson arrivals

by Ahn S., Badescu A., Cheung E., Kim Y.

Insurance: Mathematics and Economics | 2018 | Issue: 79, 26-42

Short Summary: A connection between Mathematical Risk Theory and Stochastic Claim Reserving

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Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio

by Christa Cuchiero, Walter Schachermayer and Ting-Kam Leonard Wong

Mathematical Finance | 2018

Short Summary: We study Cover's universal portfolio in the context of stochastic portfolio theory, where the market portfolio is the numeraire. Under suitable conditions, we prove that the universal portfolio is asymptotically optimal.

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Exponentially concave functions and a new information geometry

by Soumik Pal and Ting-Kam Leonard Wong

Annals of Probability | Volume 46, Number 2 (2018), 1070-1113

Short Summary: This paper uncovers deep connections between optimal transport and information geometry. It develops the dual geometry of L-divergence which extends the classical Bregman divergence. Our geometry can be applied to determine the optimal rebalancing frequency of portfolios.

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Trading Algorithms with Learning in Latent Alpha Models Mathematical Finance 

by Philippe Casgrain and Sebastian Jaimungal

Mathematical Finance | 2018

Short Summary: How does one trade when markets are driven by factors you cannot observe? This paper formulates the problem as a partial information stochastic control problem, proves various theoretical results related to the problem, solves it, uses machine learning techniques to estimate model parameters, and runs simulations to illustrate the results.

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