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Optimal Reinsurance and Investment Strategies for Insurers with regime-switching and State-Dependent Utility Function

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Journal of Systems Science & Complexity 2016年第6期29卷 1658-1682页

作者： GU Ailing LI Zhongfei School of Applied Mathematics Guangdong University of Technology Sun Yat-Sen Business School Sun Yat-Sen University

This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer,where price processes of the risky assets and wealth process of the insurer are both described by Markovian regime *** target of the insurer is assumed to maximize the expected exponential utility from her terminal wealth with a state-dependent utility *** employing the dynamic programming approach,the optimal value functions and the optimal reinsurance-investment strategies are *** addition,the impact of some parameters on the optimal strategies and the optimal value functions is analyzed,and lots of interesting results are discovered,such as the conclusion that excess-of-loss reinsurance is better than proportional reinsurance is not held in the regime-switching jump-diffusion model.

关键词： Excess-of-loss reinsurance optimal investment strategy proportional reinsurance regime-switching state-dependent utility function.

Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent regime-switching on Initial Values

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Acta Mathematica Sinica,English Series 2021年第3期37卷 389-407页

作者： Jing Hai SHAO Kun ZHAO Center for Applied Mathematics Tianjin UniversityTianjin 300072P.R.China

This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.

关键词： regime-switching state-dependent Euler–Maruyama’s approximation

Propagation of chaos and conditional McKean-Vlasov SDEs with regime-switching

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Frontiers of Mathematics in China 2022年第4期17卷 731-746页

作者： Jinghai SHAO Dong WEI Center for Applied Mathematics Tianjin UniversityTianjin300072China

We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching *** switching process is allowed to be dependent on the particle *** well-posedness and various properties of the limit conditional McKean-Vlasov SDEs are studied,and the conditional propagation of chaos is established with explicit estimate of the convergence rate.

关键词： regime-switching propagation of chaos Wasserstein distance conditional McKean-Vlasov SDEs rate of convergence

A contagion model with Markov regime-switching intensities

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Frontiers of Mathematics in China 2014年第1期9卷 45-62页

作者： Yinghui DONG Guojing WANG Financial Engineering Research Center Shanghai Jiao Tong University Shanghai 200052China Department of Mathematics and Physics Suzhou University of Science and TechnologySuzhou 215011 China Department of Mathematics and Center for Financial Engineering Soochow UniversitySuzhou 215006 China

We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.

关键词： Credit default swap (CDS) contagion model regime-switching change of measure

Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

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Science China Mathematics 2012年第11期55卷 2335-2346页

作者： QIAN LinYi WANG RongMing WANG Shuai School of Finance and Statistics East China Normal UniversityShanghai 200241China Research Center of International Finance and Risk Management East China Normal UniversityShanghai 200241China

This paper extends the model and analysis of Lin, Tan and Yang （2009）. We assume that the financial market follows a regime-switching jump-diffusion model and the mortality satisfies Levy process. We price the point to point and annual reset EIAs by Esscher transform method under Merton＇s assumption and obtain the closed form pricing formulas. Under two cases： with mortality risk and without mortality risk, the effects of the model parameters on the EIAs pricing are illustrated through numerical experiments.

关键词： compound poisson process Levy process stochastic mortality regime-switching equity-indexedannuity

Conditional coherent risk measures and regime-switching conic pricing

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Probability, Uncertainty and Quantitative Risk 2021年第4期6卷 267-300页

作者： Engel John C Dela Vega Robert J Elliott UniSA Business University of South AustraliaSA 5000 AdelaideAustralia Haskayne School of Business University of CalgaryCalgaryAlbertaT2N 1N4Canada

This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic *** price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov *** bid and ask prices of a European-type asset are then characterized using conic quantization.

关键词： Conditional coherent risk measures Markov chains regime-switching Conic finance European options Distortion functions Conic quantization

Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model

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Statistical Theory and Related Fields 2020年第2期4卷 214-227页

作者： Liming Zhang Rongming Wang Jiaqin Wei Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiPeoples Republic of China

This paper is devoted to study the proportional reinsurance/new business and investment problem under the mean-variance criterion in a continuous-time *** strategies are constrained in the non-negative cone and all coefficients in the model except the interest rate are stochastic processes adapted the filtration generated by a Markov *** the help of a backward stochastic differential equation driven by the Markov chain,we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching *** cases with one risky asset and Markov regime-switching model are considered as special cases.

关键词： Markov chain mean-variance problem non-negative constraints BSDE regime-switching

Bayesian Markov regime-switching Models for Cointegration

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Applied Mathematics 2012年第12期3卷 1892-1897页

作者： Kai Cui Wenshan Cui Department of Statistical Science Duke University Durham USA School of Science and Information Qingdao Agricultural University Qingdao China

This paper introduces a Bayesian Markov regime-switching model that allows the cointegration relationship between two time series to be switched on and off over time. Unlike classical approaches for testing and modeling cointegration, the Bayesian Markov switching method allows for estimation of the regime-specific model parameters via Markov Chain Monte Carlo and generates more reliable estimation. Inference of regime switching also provides important information for further analysis and decision making.

关键词： Cointegration regime-switching Bayesian MCMC

Pricing Catastrophe Options with Credit Risk in a regime-switching Model

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应用概率统计 2024年第4期40卷 572-587页

作者： XU Yajuan WANG Guojing Department of Mathematics and Physics Suzhou Vocational UniversitySuzhou215104China The Center for Financial Engineering and Department of Mathematics Soochow UniversitySuzhou215006China

In this paper,we consider the price of catastrophe options with credit risk in a regime-switching *** assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state *** using the measure change technique,we derive the price expressions of catastrophe put ***,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.

关键词： pricing catastrophe option credit risk regime-switching measure change