arXiv subjects

Qianqian Zhou

Publications and source records attributed to Qianqian Zhou.

8 recordsLinked to original sources

arXiv2026

Robust Optimal Reinsurance, Investment,and Surplus Allocation for Epstein-Zin Preferences

In this paper, we investigate the robust optimal reinsurance,investment,and internal surplus distribution (i.e., consumption) problem for an insurer with Epstein-Zin recursive preferences in an incomplete market. It is assumed that the insurer can allocate wealth to a financial market consisting of a risk-free asset and a risky asset, where the price process of the risky asset follows a diffusion process with a stochastic drift rate governed by an Ornstein-Uhlenbeck (O-U) process. For both the unit and non-unit elasticity of intertemporal substitution (EIS) cases, by applying the classical dynamic programming approach, we derive explicit solutions for the optimal robust reinsurance, investment,and consumption strategies and also verify that the obtained solutions indeed solve the optimal control problem. Furthermore, we compare the robust solutions with their non-robust counterparts, and the comparative results shown in the figures are consistent with economic intuition. Finally, we contrast the exact solutions with the Campbell-Shiller approximation and assess the accuracy of the approximation method.

math.OC↗

arXiv2024

A study on the $F$-distribution motivated by Chvátal's theorem

Let $X_{d_1, d_2}$ be an $F$-random variable with parameters $d_1$ and $d_2,$ and expectation $E[X_{d_1, d_2}]$. In this paper, for any $κ>0,$ we investigate the infimum value of the probability $P(X_{d_1, d_2}\leq κE[X_{d_1, d_2}])$. Our motivation comes from Chvátal's theorem on the binomial distribution.

math.PR↗

arXiv2023

Improving Urban Flood Prediction using LSTM-DeepLabv3+ and Bayesian Optimization with Spatiotemporal feature fusion

Deep learning models have become increasingly popular for flood prediction due to their superior accuracy and efficiency compared to traditional methods. However, current machine learning methods often rely on separate spatial or temporal feature analysis and have limitations on the types, number, and dimensions of input data. This study presented a CNN-RNN hybrid feature fusion modelling approach for urban flood prediction, which integrated the strengths of CNNs in processing spatial features and RNNs in analyzing different dimensions of time sequences. This approach allowed for both static and dynamic flood predictions. Bayesian optimization was applied to identify the seven most influential flood-driven factors and determine the best combination strategy. By combining four CNNs (FCN, UNet, SegNet, DeepLabv3+) and three RNNs (LSTM, BiLSTM, GRU), the optimal hybrid model was identified as LSTM-DeepLabv3+. This model achieved the highest prediction accuracy (MAE, RMSE, NSE, and KGE were 0.007, 0.025, 0.973 and 0.755, respectively) under various rainfall input conditions. Additionally, the processing speed was significantly improved, with an inference time of 1.158s (approximately 1/125 of the traditional computation time) compared to the physically-based models.

cs.LG↗

arXiv2020

Lundberg-type inequalities for non-homogeneous risk models

In this paper, we investigate the ruin probabilities of non-homogeneous risk models. By employing martingale method, the Lundberg-type inequalities of ruin probabilities of non-homogeneous renewal risk models are obtained under weak assumptions. In addition, for the periodic and quasi-periodic risk models the adjustment coefficients of the Lundberg-type inequalities are obtained. Finally, examples are presented to show that estimations obtained in this paper are more accurate and the ruin probability in non-homogeneous risk models may be fast decreasing which is impossible for the case of homogeneity.

math.PR↗

arXiv2020

Exponential bounds of ruin probabilities for non-homogeneous risk models

Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak assumptions. In addition, several risk models, including the newly defined united risk model and quasi-periodic risk model with interest rate, are studied.

math.PR↗

arXiv2020

Optimal Control of Investment for an Insurer in Two Currency Markets

In this paper, we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model. Investment in the foreign market is allowed, and therefore, the foreign exchange rate model is considered and incorporated. It is assumed that the instantaneous mean growth rate of foreign exchange rate price follows an Ornstein-Uhlenbeck process. Dynamic programming method is employed to study the problem of maximizing the expected exponential utility of terminal wealth. By soloving the correspoding Hamilton-Jacobi-Bellman equations, the optimal investment strategies and the value functions are obtained. Finally, numerical analysis is presented.

q-fin.PM↗

arXiv2020

Prokhorov distance with rates of convergence under sublinear expectations

Prokhorov distances under sublinear expectations are presented in CLT and functional CLT, and the convergence rates for them are obtained by Lindeberg method. In particular, the obtained estimate in functional CLT yields known Borovkov's estimate in classical functional CLT with explicit constant.

math.PR↗

arXiv2019

A statistical test for correspondence of texts to the Zipf-Mandelbrot law

We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count sequentially the numbers of different words in the text and get the process of the numbers of different words. Then we estimate Zipf---Mandelbrot law parameters using the same sequence and construct an estimate of the expectation of the number of different words in the text. Then we subtract the corresponding values of the estimate from the sequence and normalize along the coordinate axes, obtaining a random process on a segment from 0 to 1. We prove that this process (the empirical text bridge) converges weakly in the uniform metric on $C (0,1)$ to a centered Gaussian process with continuous a.s. paths. We develop and implement an algorithm for approximate calculation of eigenvalues of the covariance function of the limit Gaussian process, and then an algorithm for calculating the probability distribution of the integral of the square of this process. We use the algorithm to analyze uniformity of texts in English, French, Russian and Chinese.

math.ST↗