arXiv subjects

Zhenyu Shen

Publications and source records attributed to Zhenyu Shen.

4 recordsLinked to original sources

arXiv2026

Behavioral Participating Insurance: Optimal Investment under Probability Distortion and Aspiration Constraints

We study optimal investment for insurers managing participating (profit-sharing) contracts under probability distortion and probability benchmark (aspiration) constraints. The problem combines three theoretical complexities: (i) nonconcave effective utilities induced by embedded guarantees and surplus-sharing rules, (ii) probability weighting capturing behavioral aspects of long-horizon decisions, and (iii) aspiration-type constraints formalizing solvency requirements. Using quantile formulations and concavification techniques, we derive explicit closed-form solutions for optimal terminal wealth and trading strategies in both complete and incomplete Black-Scholes markets. Our utility class accommodates the piecewise hyperbolic absolute risk aversion (PHARA) family and covers nonconcavities arising naturally in insurance contexts. The framework reveals how probability distortion weakens lock-in behavior and induces time inconsistency: under inverse S-shaped distortions, insurers overestimate upside probabilities and increase risky investment relative to undistorted benchmarks. Asymptotic analysis and numerical illustrations demonstrate regime switches in optimal policies driven by regulatory thresholds and capital constraints. Our results extend the hope-fear-aspirations framework of He and Zhou (2016) and provide practical insights for managing insurance balance sheets under behavioral preferences and solvency constraints.

q-fin.MF↗

arXiv2026

Dynamic Lagrange Multipliers in a Non-concave Utility Framework

In continuous-time portfolio selection for non-concave utility functions, the martingale duality approach is widely adopted in complete markets, while the dynamic programming approach may sometimes lead to singular solutions of the Hamilton-Jacobi-Bellman (HJB) equation. We propose "dynamic Lagrange multipliers" in a non-concave utility framework, bridging two approaches and demonstrating that the Lagrangian multiplier function (in the martingale duality approach) equals the conjugate dual point related to the value function (in dynamic programming), which is exactly its partial derivative with respect to wealth. Moreover, the dynamic multiplier process exhibits homogeneity via the optimal wealth and pricing kernel processes, offering intuitive economic interpretations as a dynamic shadow price of the envelope theorem. Finally, classical optimal results are recovered and numerically validated by non-concave utility examples.

math.OC↗

arXiv2024

PSAHARA Utility Family: Modeling Non-monotone Risk Aversion and Convex Compensation in Incomplete Markets

In hedge funds, convex compensation schemes are adopted to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth level is low. Combining these two ingredients, we study the optimal control strategy of the manager in incomplete markets. Generally, we propose a wide family of utility functions, the piecewise symmetric asymptotic hyperbolic absolute risk aversion (PSAHARA) utility, to model the two ingredients, containing both non-concavity and non-differentiability as some abnormalities. Technically, we propose an additional assumption and prove concavification techniques of non--concave utility functions with a left unbounded domain in incomplete markets. Next, we derive an explicit optimal control for the family of PSAHARA utilities. This control is expressed into a unified four-term structure, featuring the asymptotic Merton term. Furthermore, we provide a detailed asymptotic analysis and numerical illustration of the optimal portfolio. We obtain several key insights, including that the convex compensation still induces a great risk-taking behavior in the case that the preference is modeled by SAHARA utility. Finally, we conduct a real-data analysis of the U.S. stock market under the above model and conclude that the PSAHARA portfolio is very risk-seeking and leads to a high return and a high volatility.

math.OC↗

arXiv2015

We Can Track You If You Take the Metro: Tracking Metro Riders Using Accelerometers on Smartphones

Motion sensors (e.g., accelerometers) on smartphones have been demonstrated to be a powerful side channel for attackers to spy on users' inputs on touchscreen. In this paper, we reveal another motion accelerometer-based attack which is particularly serious: when a person takes the metro, a malicious application on her smartphone can easily use accelerator readings to trace her. We first propose a basic attack that can automatically extract metro-related data from a large amount of mixed accelerator readings, and then use an ensemble interval classier built from supervised learning to infer the riding intervals of the user. While this attack is very effective, the supervised learning part requires the attacker to collect labeled training data for each station interval, which is a significant amount of effort. To improve the efficiency of our attack, we further propose a semi-supervised learning approach, which only requires the attacker to collect labeled data for a very small number of station intervals with obvious characteristics. We conduct real experiments on a metro line in a major city. The results show that the inferring accuracy could reach 89\% and 92\% if the user takes the metro for 4 and 6 stations, respectively.

cs.CR↗