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Xiang Cheng - One of the best experts on this subject based on the ideXlab platform.
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approximation of a class of non zero sum Investment and reinsurance games for regime switching jump diffusion models
Nonlinear Analysis: Hybrid Systems, 2019Co-Authors: Xiang ChengAbstract:Abstract This work develops an approximation procedure for a class of non-zero-sum stochastic Differential Investment and reinsurance games between two insurance companies. Both proportional reinsurance and excess-of loss reinsurance policies are considered. We develop numerical algorithms to obtain the approximation to the Nash equilibrium by adopting the Markov chain approximation methodology. We establish the convergence of the approximation sequences and the approximation to the value functions. Numerical examples are presented to illustrate the applicability of the algorithms.
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approximation of a class of non zero sum Investment and reinsurance games for regime switching jump diffusion models
arXiv: Optimization and Control, 2018Co-Authors: Xiang ChengAbstract:This work develops an approximation procedure for a class of non-zero-sum stochastic Differential Investment and reinsurance games between two insurance companies. Both proportional reinsurance and excess-of loss reinsurance policies are considered. We develop numerical algorithms to obtain the Nash equilibrium by adopting the Markov chain approximation methodology and applying the dynamical programming principle for the nonlinear integro-Differential Hamilton-Jacobi-Isaacs (HJI) equations. Furthermore, we establish the convergence of the approximation sequences and the approximation to the value functions. Numerical examples are presented to illustrate the applicability of the algorithms.
Alain Bensoussan - One of the best experts on this subject based on the ideXlab platform.
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a class of non zero sum stochastic Differential Investment and reinsurance games
Automatica, 2014Co-Authors: Alain Bensoussan, Chi Chung Siu, Sheung Chi Phillip Yam, Hailiang YangAbstract:Abstract In this article, we provide a systematic study on the non-zero-sum stochastic Differential Investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an Investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/Investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.
Hailiang Yang - One of the best experts on this subject based on the ideXlab platform.
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a class of non zero sum stochastic Differential Investment and reinsurance games
Automatica, 2014Co-Authors: Alain Bensoussan, Chi Chung Siu, Sheung Chi Phillip Yam, Hailiang YangAbstract:Abstract In this article, we provide a systematic study on the non-zero-sum stochastic Differential Investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an Investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/Investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.
Timothy H Parker - One of the best experts on this subject based on the ideXlab platform.
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genetic benefits of mate choice separated from Differential maternal Investment in red junglefowl gallus gallus
Evolution, 2003Co-Authors: Timothy H ParkerAbstract:Females may choose more attractive mates to obtain better viability or attractiveness genes for their offspring. A number of studies have demonstrated a positive relationship between paternal attractiveness and offspring quality. However, this pattern could be due to inheritance of paternal genes and/or it could be due to increased maternal Investment in the offspring of more attractive males. To isolate female responses to male appearance from paternal genetic effects, I housed female red junglefowl (Gallus gallus) with vasectomized (sterile) males and artificially inseminated them. Male junglefowl with larger combs are more attractive to females. Females laid more eggs when housed with a large-combed, as opposed to a small-combed, vasectomized mate. Neither egg volume nor offspring body condition was associated with comb size of the mother's vasectomized mate. Paternal genetics appeared important. Body condition and comb size were greater for the sons of large-combed sperm donor males. This is consistent with the hypothesis that genetic benefits to offspring maintain female preference for the most ornate males. It is possible that greater body condition and comb size in sons of large-combed sires was not caused by genetic differences, but instead was due to compounds in the ejaculate of large-combed sperm donors inducing greater reproductive Investment from females. However, females artificially inseminated by large-combed males did not produce more or larger eggs than females artificially inseminated by small-combed males, and thus there is no other evidence consistent with ejaculate-induced Differential Investment. Furthermore, only in older chicks was body condition significantly related to sire comb size, suggesting genetic rather than Differential Investment mechanisms.
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genetic benefits of mate choice separated from Differential maternal Investment in red junglefowl
2003Co-Authors: Gallus Gallus, Timothy H ParkerAbstract:Females may choose more attractive mates to obtain better viability or attractiveness genes for their offspring. A number of studies have demonstrated a positive relationship between paternal attractiveness and offspring quality. However, this pattern could be due to inheritance of paternal genes and/or it could be due to increased maternal Investment in the offspring of more attractive males. To isolate female responses to male appearance from paternal genetic effects, I housed female red junglefowl (Gallus gallus) with vasectomized (sterile) males and artificially inseminated them. Male junglefowl with larger combs are more attractive to females. Females laid more eggs when housed with a large-combed, as opposed to a small-combed, vasectomized mate. Neither egg volume nor offspring body condition was associated with comb size of the mother's vasectomized mate. Paternal genetics appeared important. Body condition and comb size were greater for the sons of large-combed sperm donor males. This is consistent with the hypothesis that genetic benefits to offspring maintain female preference for the most ornate males. It is possible that greater body condition and comb size in sons of large-combed sires was not caused by genetic differences, but instead was due to compounds in the ejaculate of large-combed sperm donors inducing greater reproductive Investment from females. However, females artificially inseminated by large-combed males did not produce more or larger eggs than females artificially inseminated by small-combed males, and thus there is no other evidence consistent with ejaculate-induced Differential Investment. Furthermore, only in older chicks was body condition significantly related to sire comb size, suggesting genetic rather than Differential Investment mechanisms.
Hoi Ying Wong - One of the best experts on this subject based on the ideXlab platform.
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robust non zero sum stochastic Differential Investment reinsurance game
Social Science Research Network, 2016Co-Authors: Chi Seng Pun, Hoi Ying WongAbstract:This paper considers the non-zero-sum stochastic Differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal Investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free asset, and manages her own risks by purchasing reinsurance with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her counterparty. The two AAIs' decisions influence each other through the insurers' relative performance concerns and the correlation between their surplus processes. We establish a general framework of Nash equilibrium for the associated non-zero-sum game with model uncertainty. For the representative case of exponential utilities and the Heston model, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations.