My general interests are in probability theory and stochastic processes. Currently, I am focusing on the theory of anticipating stochastic integrals with Prof Hui-Hsiung Kuo and large deviation principles with Prof Padmanabhan Sundar. To understand the motivation behind large deviation principles, you can check out my short write up on my blog.

My other interests include mathematical finance, machine learning, optimization, numerical analysis, differential equations, and philosophy of mathematics.

I was very interested in programming as a kid, and I have recently started rediscovering it. Currently, I am trying to solve the easiest problems in Project Euler using Julia. I post my solutions in my GitHub repository.

• Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai (2018). “Stochastic Differential Equations with Anticipating Initial Conditions”. In: Communications on Stochastic Analysis 12.4. DOI: 10.31390/cosa.12.4.06. URL: https://digitalcommons.lsu.edu/cosa/vol12/iss4/6.

• 2020-01-17 (JMM2020, 20 min): talk on Stochastic Differential Equations with Anticipating Initial Conditions

• 2019-04-05 (LSU, 50 min): General exam talk

• 2019-08-22 (LSU, 25 min): A research talk on Introduction to Probability and Stochastic Analysis to first-year graduate students

Details

🎓 Doctorate

🏫 Louisiana State University

🏬 Department of Mathematics and Graduate School

📍 Baton Rouge, LA 🇺🇸

📆 2016-09-15 to 2022-05-20

㎬ 4/4

Dissertation: Anticipating Stochastic Integrals and Related Linear Stochastic Differential Equations

Courses

• • Analysis (ℝ ∪ ℂ ∪ functional)

  • Probability theory and stochastic analysis

  • Applied stochastic analysis

  • Gaussian measures on Banach spaces

  • Large deviation principles

  • Differential equations (ordinary ∪ partial ∪ stochastic)

  • Optimization

  • Abstract algebra

  • Topology (point-set ∪ algebraic ∪ differential)

  • Mathematical logic

  • Analytical philosophy (mathematics ∪ science)

  • Communicating mathematics

  • Mathematical statistics

  • Finance risk management

Received as a part of my doctoral journey.

Details

🎓 Master of Science

🏫 Louisiana State University

🏬 Department of Mathematics and Graduate School

📍 Baton Rouge, LA 🇺🇸

📆 2016-09-15 to 2018-05-12

㎬ 4/4

My master's degree was in the area of mathematical modeling in the Erasmus Mundus M.Sc. program "MathMods". The program had the following structure.

1. Semester 1 in the University of L’Aquila was focused on theoretical aspects of applied mathematics.

2. Semester 2 in the University of Hamburg was focused on numerical methods for solving partial differential equations, optimization, and machine learning.

3. Semester 3 in the University of L’Aquila focused on my specialization, which was stochastic modeling and its applications, particularly in mathematical finance.

4. Semester 4 in the University of L’Aquila was devoted to my thesis.

Details

🎓 Master of Science

🏫 MathMods (Università degli Studi dell'Aquila 🇮🇹 and Universität Hamburg 🇩🇪)

📍 L'Aquila, AQ, 🇮🇹 and Hamburg, 🇩🇪

📆 2013-09-09 to 2015-10-23

㎬ 3.5/4 (110/110 cum laude)

Thesis

🧙🏼‍♂️ Prof. Fabio Antonelli

📕 Singular Points method for pricing exotic path-dependent options

The Singular Points method is a tree-based method that was introduced by Marcellino Gaudenzi and Antonino Zanette to price exotic path-dependent options like Asian options and cliquet options. The method allows for bounded approximations, which in turn enables a reduction in the order of complexity from exponential time to polynomial time, with guaranteed convergence. We studied the extensibility of the method to similar options, and showed that the method can neither be extended to American Asian options with geometric mean, nor to local volatility cases. We also found out that the experimental running time in the case of cliquet options is O(m²), where m is the number of time steps.

Projects

• • Studied the coupon collector’s problem and its generalizations under Prof. Dr. Ingenuin Gasser.

  • Worked on “Decoding the Human Brain” (Kaggle) under Morteza Alamgir.

Achievements

Along with a 90% reduction in tuition fees, I was awarded a scholarship by the Gran Sasso Science Institute in Italy for academic merit, which I was able to retain throughout the extent of my studies by consistently scoring above 90% on average.

After completing my schooling, I studied chemical engineering in BITS Pilani for four years. I realized that I wanted more exposure to abstract ideas. During the last semester, I interned at Oracle Financial Services.

Details

🎓 Bachelor of Engineering (Honours)

🏫 Birla Institute of Technology & Science, Pilani

🏬 Department of Chemical Engineering

📍 Goa 🇮🇳

📆 2008-01-04 to 2011-12-14

㎬ 8.53/10

Thesis

🧙🏼‍♂️ Prof. Srinivas Krishnaswamy

I studied the modeling and simulation of Savonius Turbines. This was a computational fluid dynamic study on the efficiency and viability of Savonius wind turbines as small power generation systems (less than 1 kW). Parameters considered were the angular position, radius and the number of blades, and tip-speed ratio. We performed the simulation and analysis using COMSOL Multiphysics®.

I attended the three-month long online minicourse on probabilistic methods applied primarily to models of statistical mechanics.

Details

🏫 Mathematics Department at the University of British Columbia

📍 online

📆 2020-05-18 to 2020-08-13