arXiv subjects

Pengyu Wei

Publications and source records attributed to Pengyu Wei.

9 recordsLinked to original sources

arXiv2026

Deep Penalty Methods: A Class of Deep Learning Algorithms for Solving High Dimensional Optimal Stopping Problems

We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE framework proposed by \cite{weinan2017deep}, which leads us to coin the term "Deep Penalty Method (DPM)" to refer to our algorithm. We show that the error of the DPM can be bounded by the loss function and $O(\frac{1}λ)+O(λh) +O(\sqrt{h})$, where $h$ is the step size in time and $λ$ is the penalty parameter. This finding emphasizes the need for careful consideration when selecting the penalization parameter and suggests that the discretization error converges at a rate of order $\frac{1}{2}$. We validate the efficacy of the DPM through numerical tests conducted on a high-dimensional optimal stopping model in the area of American option pricing. The numerical tests confirm both the accuracy and the computational efficiency of our proposed algorithm.

q-fin.MF↗

arXiv2026

Constrained portfolio optimization in a life-cycle model: A deep pricing kernel approach

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize their consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, with the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint as special cases. We build the artificial markets to solve this problem by manipulating the compensated drift terms of the underlying assets to meet the trading constraints. By dual transform, we propose a deep pricing kernel approach to compute tight lower and upper bounds for the primal problem, which can be used when the value function lacks an explicit solution due to the pricing kernel's conditional expectation. Finally, we conclude that when considering the trading constraints, the individual will reduce their consumption, demand for life insurance and annuities, and wealth levels due to the restricted market.

q-fin.PM↗

arXiv2026

Optimal Life Insurance Decision in Mean-Variance DC Management with Mortality Improvements

This paper studies the investment and insurance strategies of defined-contribution (DC) pension plans under the mean-variance framework. We consider a stochastic environment with time-varying interest rates, contributions, and mortality risk. The DC plan members are allowed to decide their bond and stock allocations, as well as their life insurance coverage. Adopting the martingale approach, we derive the closed-form optimal strategies and the mean-variance efficient frontier. Further numerical analysis investigates how mortality improvements affect investment and insurance decisions, as well as the sensitivity of the optimal decision to market parameters. Our analysis suggests that longevity raises expectations of future contributions, allowing pension members to adopt a less risky investment strategy. Meanwhile, insurance strategy shifts toward early adulthood to protect the high value of future income and decreases significantly at later ages. Moreover, we conduct sensitivity analyses on the target expected wealth, market price of risk, and contribution growth. These findings provide practical guidance for pension members on investment and offer insights for the design of DC pension plans.

q-fin.PM↗

arXiv2026

Non-concave Corporate Management with Option Incentives under Value-at-Risk Constraint

This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal terminal firm value on the concave envelope of the objective function. Applying the quantile formulation and the martingale approach, we can derive explicit solutions for optimal effort, terminal firm value, and project choice. The optimal terminal firm value can be divided into nine cases by carefully discussing the choices of VaR floor and tail probability. Compared with the benchmark case, we find that a VaR manager will smooth terminal firm value across states, reducing it in good states while supporting it in adverse states. Moreover, a VaR requirement generally improves downside protection and reduces bankruptcy probability when the VaR floor is low or moderate. However, when the VaR floor is sufficiently high, it can increase bankruptcy probability and induce gambling-for-recovery behavior in adverse states. Our sensitivity analysis indicates that greater managerial effort uniformly improves firm value. Moreover, more incentive options make managers more responsible, leading to a smoother terminal firm value across states. In contrast, a high fixed salary makes the manager less responsible and ultimately causes a more dispersed firm value.

q-fin.MF↗

arXiv2026

Single-shot in situ pulse-duration measurement using plasma grating

Accurate measurement of the pulse duration of ultrashort, ultra-intense laser pulses at focus is essential for strong-field science. Most existing diagnostics, however, cannot allow direct in situ measurement in the focal region because of damage-threshold limits and unavoidable spatial averaging. We present a direct single-shot far-field diagnostic based on a plasma grating. In this method, the pulse duration is encoded in the axial length of an interference-written plasma grating and retrieved from the corresponding Bragg-diffraction signal. Comparison with near-field (pre-focus) autocorrelator measurements and far-field (at-focus) scanning measurements confirms single-shot pulse-duration retrieval in the focal region over 35-130 fs, and the method remains effective at a peak intensity of $\sim 10^{16}{\rm W/cm^2}$. In principle, the measurable range can be extended to 15-300 fs and to higher peak intensities. The method is insensitive to the laser central wavelength and offers a practical approach to far-field diagnostics in high-power laser systems.

physics.optics↗

arXiv2024

Optimal life insurance and annuity decision under money illusion

This paper investigates the optimal consumption, investment, and life insurance/annuity decisions for a family in an inflationary economy under money illusion. The family can invest in a financial market that consists of nominal bonds, inflation-linked bonds, and a stock index. The breadwinner can also purchase life insurance or annuities that are available continuously. The family's objective is to maximize the expected utility of a mixture of nominal and real consumption, as they partially overlook inflation and tend to think in terms of nominal rather than real monetary values. We formulate this life-cycle problem as a random horizon utility maximization problem and derive the optimal strategy. We calibrate our model to the U.S. data and demonstrate that money illusion increases life insurance demand for young adults and reduces annuity demand for retirees. Our findings indicate that the money illusion contributes to the annuity puzzle and highlights the role of financial literacy in an inflationary environment.

q-fin.PM↗

arXiv2024

Irreversible investment under weighted discounting: effects of decreasing impatience

This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhibit decreasing impatience, including the hyperbolic discount function as a special case. By deriving the Bellman system that characterizes the equilibrium, we establish the framework for analyzing investment behaviors of agents subject to decreasing impatience. From an economic perspective, we demonstrates that decreasing impatience prompts early investment. From a technical standpoint, we warn that decreasing impatience can lead to the failure of the smooth pasting principle.

q-fin.MF↗

arXiv2022

Relative growth rate optimization under behavioral criterion

This paper studies a continuous-time optimal portfolio selection problem in the complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor concerns about the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of M-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. By the martingale method, concavification and quantile optimization techniques, we derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to Zhang et al where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor's risk tolerance level is high and the market states are bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs.

q-fin.PM↗

arXiv2021

Dynamic growth-optimum portfolio choice under risk control

This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth up to the concave envelope of a certain function, and obtain analytical expressions for the optimal wealth and portfolio policy when the risk is measured by VaR or ES. In addition, we find that the efficient frontier is a concave curve that connects the minimum-risk portfolio with the growth optimal portfolio, as opposed to the vertical line when WVaR is used on terminal wealth. Our results advocate the use of mean-WVaR criterion for log-returns instead of terminal wealth in dynamic portfolio choice.

q-fin.RM↗