David Ricardo Montalván Hernández

Actuary / M.Sc. Computer Science

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Some of my background

Bachelor degree in actuarial science
Universidad Nacional Autónoma de México (UNAM)

Specialized in Mathematical Finance

Relevant Courses

  • Probability I (Univariate distributions)
  • Probability II (Multivariate distributions)
  • Stochastic Processes (Stochastic calculus)
  • Analysis (Measure theoretic probability)
  • Statistics I (Parametric statistics)
  • Statistics II (Non-parametric statistics)
  • Statistics III (Survival analysis and time series)
  • Operations Research (Linear programming)
  • Programming I & II (C/C++/R)


Merton's jump diffusion model for pricing european options: A martingale approach

Objective: Using the equivalent martingale approach, find the value of an european option, \(V(t,T, S_t) \), when $$dS_t = \left(\alpha - \lambda \kappa \right)S_{t}dt + \sigma S_{t}dW_{t} + S_{t^-}dQ_{t}$$

$$V(t, T, S_t) = e^{-(T-t)} E_{\mathbb{P}} \left[ V(T, S_T)| \mathcal{F}_t \right]$$

Master's degree in Computer Science
Instituto Politécnico Nacional (IPN)

Artificial Intelligence Laboratory

Relevant Courses

  • Theory of Computation
  • Algorithms
  • Artificial Intelligence
  • Statistical Machine Learning
  • Pattern Recognition
  • Evolutionary Optimization Algorithms


Automated learning of trading rules for the stock market

Objective: Learn a set of IF-THEN rules to generate a trading strategy that can beat the buy-and-hold strategy proposed by the Efficient Market Hypothesis.

  • Proposed a novel labelling methodology for financial time series (evolutionary algorithm).
  • CN2 and AQ20 algorithms for learn the set of rules.
  • Obtained mixed results
  • Hard to cope with highly uncertain environments.

Job Experience

  • Teacher Assistant @ Universidad Nacional Autónoma de México (UNAM) - August 2012 / June 2013.
  • Stock Indexes Analyst @ Mexican Stock Exchange - July 2013 / February 2015.
  • Economic Data Analyst @ Bloomberg L.P. - August 2015 / August 2017.
  • Professor @ Instituto Tecnológico Autónomo de México (ITAM) - October 2019 / June 2020.

Research Directions

The fields I would like to explore are related to the responsible use of AI:

  • Ethical AI.
  • Interpretable/Explainable AI.
  • Causality (Judea Pearl's work).

Related to the previous fields, currently I'm researching on:

  • Probabilistic Inductive Logic Programming.
  • Probabilistic Graphical Models.
  • Tractable Probabilistic Models.
  • Probabilistic Programming.
  • Reasoning and Knowledge Representation.

Other fields I would like to explore are:

  • Evolutionary Algorithms.
  • Data Efficient Models.
  • Monte Carlo Methods (MCMC, HMC, LMC, ...).
  • Topological Data Analysis.
  • Cognitive Science.
  • Philosophy of AI (Aiming to a human-level intelligence?)
  • Pedagogy in Computer Science.

Two tentative research proposals

Causality in time series

  • David Hume (A Treatise of Human Nature) says that one of the requirements for causality is temporal precedence $$X_{t^{-}} \rightarrow Y_{t}$$
  • The Holy Grail in finance/economics
  • Can we extend do-calculus to time series?

Embeding previous knowledge in tractable models

  • Under certain restrictions, sum product networks can make inference a tractable computation
  • Is not easy to embed previous knowledge on them
  • Is it possible? How to do so?
  • Is there any tractable model capable of this?


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