Most scholars of my generation have been instilled with the Newtonian view of an orderly, causal, and trajectorial world, and further framed by all the deterministic toolkits of Calculus, Linear or Commutative Algebra, Differential Equations, Differential Geometry, etc. It has become quite a challenge to engender a stochastic view of the complex world surrounding us, and to unleash the power of all the classical tools to the wild arena of stochasticity. The stochastic worldview was even hard for Einstein to reconcile to, some say.
From Imaging/Vision to Quant Finance, the stochastic approach offers a language, a model, and a solution.
[Disclaimer: The header background image is copied from NASA's James Webb space telescope]
(2024) Jackie Shen, White Paper - DQT Transaction Cost Models (TCM) (online), a white paper for the proprietary TCM of production quality, by the Deep QuanTech, March, 2024. Try out the free Web GUI.
[Summary] Transaction Cost Models (TCM) (or also called Liquidity Cost Models (LCM)) are fundamental for forecasting pre-trade shortfalls, computing or assessing broker-dealer commissions or markups, and developing the new generation of portfolio optimizers that incorporate liquidity qualities and liquidation costs, etc. A TCM model projects the expected liquidation costs out of the jungle of multiple uncertain stochastic factors of Brownian prices, market volumes, security volatilities, bid/ask spreads, and so on.
From top investment banks to major execution agency houses, traditional TCMs can only be calibrated from the massive individual trading data privately owned by these entities. But the big data cannot overcome the curse of the extremely low signal-to-noise ratios (SNR). In this work, for the first time in the financial world, we are able to deliver a TCM model of production quality, based entirely on all available sources of public data.
[Novelty] A TCM model based solely on public data has never been thought possible in finance, before us.
(2024) Jackie Shen, White Paper - DQT Crypto Factor Models (online), a white paper for the first publicly released crypto factor model of production quality, by the Deep QuanTech, February, 2024.
[Summary] From Nobel Laureates to Wall St, the notion of systematic factors is critical for deciphering and disentangling the stochastic complexity behind economies or the financial world. It allows to make strategic and systematic investment decisions, as well as to effectuate stylized risk controls. In this work, with the seamless integration of Quant skills and Tech toolkits, we deliver the first stochastic factor model of production quality for the ever evolving universe of cryptos.
[Novelty] The novel metric of entropy of the entire universe introduced here is profound, in our opinion.
(2021) J. Shen, "Bucketed PCA neural networks with neurons mirroring signals (arXiv)" (or via SSRN.3897477)
[Keywords] Interpretable AI, supervised learning, (artificial) neurons, DNN, mirroring, PCA, transforms, bucketing, error correction.
(2020) J. Shen, A stochastic LQR model for Child Order Placement (COP) in algorithmic trading. SSRN #3574365.
[Keywords] Child order placement, dynamic programming, LQR, delay cost, spread, impact cost, information leakage, Poisson hits, passive, aggressive, Bellman equation, optimal policy.
(2017) J. Shen, Hybrid IS-VWAP dynamic algorithmic trading via LQR. SSRN #2984297.
[Keywords] Dynamic programming, LQR, implementation shortfall (IS), VWAP, slippage, spread, delay cost, impact cost, stochastic price dynamics, Bellman equation, optimal policy.
(2009) J. Shen, Least-square halftoning via human vision system and Markov gradient descent (LS-MGD): Algorithm and analysis, SIAM Review, 51(3):567-589, 2009. The PDF file. A sample figure.
[Keywords] Halftoning, Human Vision System (HVS), mixing, entropy, least square, stochastic gradient descent, Markov random walk, random fields, convergence analysis, blue noise.
(2006) J. Shen, A stochastic-variational model for *soft* Mumford-Shah segmentation, Int'l J. Biomedical Imaging, vol. 2006, Article ID 92329, 2006 (Open Access). The PDF file (at nih.gov). Sample figure A. Sample figure B.
[Keywords] soft vs. hard, Mumford-Shah, pattern, fuzzy ownership, probability simplex, Modica-Mortola, phase-field, Egorov's theorem, existence theorems, AM algorithm.
(2005) J. Shen and Y.-M. Jung, Geometric and stochastic analysis of reaction-diffusion patterns , Int'l J. Pure Applied Math., 19(2):195-248, 2005. The PDF file.
[Keywords] data mining, pattern, Turing instability, reaction, diffusion, entropy, skewness, kurtosis, isoperimetric ratio, curvature measure.
(2001) J. Shen, On the singular values of Gaussian random matrices, Linear Alg. Appl., 326(1-3), 1-14, 2001.
[Keywords] Random matrices, singular values, Gaussian ensemble, Wishart ensemble, thermodynamic limit, pseudo-Coulomb gas, circle law, and quadrant law.
(2000) Gian-Carlo Rota and Jianhong Shen, On the combinatorics of cumulants, J. Comb. Theory (A) , 91(1), 283-304, 2000.
[Keywords] Cumulants, umbrae, exponential (moment) generating function, Schur symmetric functions, orthogonal polynomials, binomial sequence, Moebius inversion.
In memory of my beloved mentor and friend - Gian-Carlo Rota (1932-1999).
(2000) J. Shen, A geometric approach to ergodic non-homogeneous Markov chains, in "Wavelet Analysis and Multiresolution Methods", Lecture Notes in Pure and Applied Mathematics, 212, pp. 341-366, 2000.
[Keywords] Weak Ergodicity, Markovian, Scrambling Matrix, Hajnal, Simplex Transform, Contraction, Rota-Strang Joint Spectral Radius.
(1998) G.-C. Rota, J. Shen, and B. D. Taylor, All polynomials of binomial type are represented by Abel polynomials, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (IV), 25(3-4), pp. 731-738, 1998.
[Keywords] Moment generating functions, symbolic random variables (i.e. umbrae), binomial polynomials, Lagrange inversion. In memory of De Giorgi.