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.

Read more

 


 

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

Read more

 


 

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.

Read more

 


 

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.

Read more

 


 

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.

Read more