I am Cai Wu (吴偲), a senior undergraduate student pursuing a major 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 operations research, currently with a concentration on financial engineering (quantitative finance, financial mathematics). Specifically, I am interested in detailed topics including option pricing, market microstructure and portfolio optimization, methodologically preferring stochastic modeling, mathematical optimization and machine learning. I am open to other fields like revenue management, business analytics or supply chain management in the future.

Meanwhile, I have a broader passion for the application of mathematical knowledge, statistical tools and coding skills in fields such as economics and actuarial science. My ultimate goal is the combination of theoretical findings and practical applications to provide assistance for practitioners, institutions and organizations.

I am currently seeking for a Ph.D. position in aforementioned fields.

Education

• B.S. Economics, Fudan University (Shanghai, China), Sept. 2020 - Jun. 2024 (expected)
• Visiting student, University of California, Berkeley (Berkeley, CA), Jan. 2023 - May. 2023

Publications and Preprints

• Explicit solution to the economic index of riskiness, with Zhenyu Cui and Lingjiong Zhu. Economics Letters, Volume 232, November 2023, 111343. Also available at: [ResearchGate]
  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.
• Variance optimality of empirical martingale simulation estimators, with Zhenyu Cui, Yanchu Liu, Ruodu Wang and Lingjiong Zhu. Submitted to Management Science. 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.
• VIX options valuation via continuous-time Markov chain approximation and Ito-Taylor expansion, with Zhenyu Cui, Chihoon Lee and Mingzhe Liu. Submitted to Journal of Derivatives.
  Abstract

  We propose a novel analytical method to valuate 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 valuate 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.
• An exact explicit solution to the adjustment coefficient in risk theory, with Zhenyu Cui. Submitted to European Actuarial Journal.
  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.