### 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)

## Thesis

#### 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

## Thesis

#### 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.

## 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?

# Questions?

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