I am Cai Wu (吴偲), a 1st-year PhD student at the Department of Statistics and Applied Probability at University of California, Santa Barbara. Previously, I obtained my Bachelor of Science in Economics at the School of Economics with a minor in Financial Mathematics at the School of Mathematical Sciences, Fudan University in China.

My primary research interest lies in Quantitative Finance, with a particular concentration on Decentralized Finance (DeFi) and Financial Technology (FinTech). Recently, I have also developed an interest in E-sports Analytics, especially in studying game mechanics and player performance in first-person shooter (FPS) games such as Counter-Strike 2 and Valorant—as an avid gamer myself, I find this area both intellectually engaging and personally exciting.

Please feel free to reach out if you would like to discuss research, music, or anything else you find interesting!

My name is pronounced like “Ts-eye Woo.” Starting in March 2026, I will publish under the name Cai Kure Wu. “Kure” is the romanized Japanese of my family name.

Here’s the newest version of my CV updated on 2/27/2026: How’s your day!

Education

• Ph.D. in Statistics and Applied Probability, University of California, Santa Barbara, (Santa Barbara, CA), Sept. 2025 - Now
• B.S. in Economics, Fudan University (Shanghai, China), Sept. 2020 - Jun. 2025
• Visiting student, University of California, Berkeley (Berkeley, CA), Jan. 2023 - May. 2023

Working Papers

• Analyzing Shot Dispersion and Reset Mechanics in Competitive Gaming. Submitted.

• Adding and subtracting Merton: A new approach for optimal portfolio and consumption, with Zhenyu Cui, Kailin Ding, and Yanchu Liu.

• Variance optimality of empirical martingale simulation estimators, with Zhenyu Cui, Yanchu Liu, Ruodu Wang and Lingjiong Zhu. Also available at: [ResearchGate]

  Abstract

  In this paper, we provide the theoretical groundwork for the optimality of the variance of the "empirical martingale simulation" (EMS) estimator first introduced in Duan and Simonato (1998). The EMS estimator is proposed to be an improvement of the traditional Monte Carlo estimator, and is shown to yield smaller variance in numerical examples in the literature. However, there is no theoretical guarantee for the superior performance as compared to the traditional Monte Carlo. This paper is the first to rigorously examine this issue and justify the benefits of the EMS estimator in reducing the asymptotic variance. We establish the conditions under which the asymptotic variance of the EMS estimator is smaller than that of the standard Monte Carlo estimator. This addresses the long-standing open problem clearly posed in Duan and Simonato (1998), Duan et al. (2001) and Yuan and Chen (2009). In particular, we show that the EMS estimator always reduces the variance of the Monte Carlo estimator for European options in the Black-Scholes model through the novel use of Stein's lemma. We also discuss when the EMS estimator is not effective in reducing the variance. Furthermore, we illustrate our theoretical findings through extensive numerical experiments.

Publications and Preprints

• VIX options valuation via continuous-time Markov chain approximation and Ito-Taylor expansion, with Zhenyu Cui, Chihoon Lee and Mingzhe Liu. Journal of Derivatives, 32(1), 11-31.
  Abstract

  We propose a novel analytical method to evaluate VIX options under the general class of affine and non-affine stochastic volatility models, which extends the current literature in particular to the realm of non-affine stochastic volatility models. The approach is based on a closed-form approximation of the VIX index through the Ito-Taylor expansion and the subsequent continuous-time Markov chain (CTMC) approximation to evaluate VIX options. The formula is in explicit closed-form and does not involve numerical (Fourier) inversions, in contrast to the existing literature. Numerical experiments with several stochastic volatility models demonstrate that it is accurate and efficient by comparing with benchmarks in the literature and Monte Carlo simulations. Empirical experiments demonstrate that in general non-affine stochastic volatility models provide better fit to the VIX options data.
• Explicit solution to the economic index of riskiness, with Zhenyu Cui and Lingjiong Zhu. Economics Letters, 232, 111343.
  Abstract

  In this paper, we develop an exact closed-form series expansion for the economic index of riskiness of general gambles in terms of moments information. Important special cases include the economic indexes of riskinesses proposed in Aumann and Serrano (2008); Bali et al. (2011); Foster and Hart (2009). Based on the closed-form formula, we characterize further theoretical properties for the economic index of riskiness. Numerical examples confirm the accuracy of the proposed closed-form formula.
• An exact explicit solution to the adjustment coefficient in risk theory, with Zhenyu Cui. Permanent working paper.
  Abstract

  In this paper, we derive an exact explicit formula for the adjustment coefficient, which is the unique positive solution of the corresponding Lundberg equation. It is a key quantity in the classical Cram ́er-Lundberg risk theory, and is a fundamental building block for the celebrated Lundberg inequality for ruin probabilities. We utilize the Lagrange inversion theorem and derive the explicit exact formula in terms of series expansions. Numerical results illustrate the accuracy of the formula.

Teaching

• PSTAT 5A (TA, UCSB): Understanding Data (Winter 2026, Fall 2025)
• PSTAT 5LS (TA, UCSB): Statistics for Life Sciences (Fall 2025)