• ## Time Synchronization on Amazon EC2

My trading bot just ceased this morning from its loyal 24/7 service. It's running on an Amazon EC2 server with Ubuntu 16.04 and I'm sure this time I'm not having an unpaid-bill issue any more. After some time digging I think I finally figure out the cause of this unexpected strike -- asynchronism.

• ## LDA and R-MDA

This is a note of Linear Discriminant Analysis (LDA) and an original Regularized Matrix Discriminant Analysis (R-MDA) method proposed by Jie Su et al, 2018. Both methods are suitable for efficient multiclass classification, while the latter is a state-of-the-art version of the classical LDA method s.t. data in matrix forms can be classified without destroying the original structure.

• ## Literature Review on Optimal Order Execution (5)

This is the fifth post on optimal order execution. Based on Almgren and Chriss (2000), today we attempt to estimate the market impact coefficient $\eta$. Specifically, for high-frequency transaction data, we have the approximation $dS = \eta\cdot dQ$ and thus can easily estimate it by the method of Ordinary Least Squares (OLS), using the message book data provided by LOBSTER.

• ## Literature Review on Optimal Order Execution (4)

Today we implement the order placement strategy in Almgren and Chriss (2000) s.t. for a certain order size $Q$, we can estimate the probability to perform the optimal strategy in the paper within time horizon of $T$.

• ## Parameter Estimation of Brownian motions by Method of Moments

How to estimate the parameters of a geometric Brownian motion (GBM)? It seems rather simple but actually took me quite some time to solve it. The most intuitive way is by using the method of moments.

• ## Literature Review on Optimal Order Execution (3)

Here I'm trying to write something partly based on Cont's first model in the previous post. I plan to skip the Laplace transform and go for Monte Carlo simulation. Also, I'm trying to abandon the assumption of unified order sizes. To implement that, I need to shift from a Markov chain which is supported by discrete spaces, onto some other stochastic process that is estimatable. Moreover, although I actually considered supervised learning for this problem, I gave it up at last. This is because my model is inherently designed for high frequency trading and thus training for several minutes each time would be intolerable.

• ## Literature Review on Optimal Order Execution (2)

Today, I'll continue introducing papers about optimal order execution and particularly, in this post I'll mainly walk through six papers by Rama Cont, respectively in 2010 and 2018. Professor Cont is renowned for his indepth research in stochastic analysis, stochastic processes and mathematical modeling in quantitative finance. He's written dozens of papers concerning the order book dynamics by building rigorous mathematical models.

• ## Hexo Actually Supports Markdown Flowchart

It is supported by the package hexo-filter-flowchart: