This paper considers the problem of minimizing the VaR and CTE of an insurer＇s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, th...This paper considers the problem of minimizing the VaR and CTE of an insurer＇s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, the authors give the explicit reinsurance forms and the minimal VaR and CTE of retained risk in the case of quota-share after stop-loss reinsurance and the case of stop-loss afterquota-share reinsurance respectively. Finally, the authors conclude that the quota-share after stop-loss is a better reinsurance strategy than stop-loss after quota-share to minimize the VaR and CTE with a same constrained reinsurance premium. And the pure stop-loss reinsurance is preferred for an insurer with a high level regulatory requirement.展开更多
Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of...Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.展开更多
In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate ...In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.展开更多
We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. E...We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.展开更多
Academic research has identified several factors that affect price movements;however,the scenario changes abruptly in the case of very short time price changes(VSTPC).This topic is not specifically examined in the exi...Academic research has identified several factors that affect price movements;however,the scenario changes abruptly in the case of very short time price changes(VSTPC).This topic is not specifically examined in the existing literature;nonetheless,the behavior of the market microstructure is quite different at the subsecond scale.Indeed,below a certain psychological time threshold,most factors typically influencing price changes cease to apply.This paper analyzes several parameters considered to affect price changes and identifies four of them as potentially influencing VSTPC.These factors are previous volatility,scarce liquidity,high quantity exchanged,and stop-loss(SL)orders(seldom mentioned in the literature).These four parameters are examined by means of a mathematical model,audit trail data analysis,Granger-causality testing,and agent-based model.The results of these four techniques converge to suggest a nonlinear combination of previous volatility,liquidity,and SL orders as the main causes of excess volatility.However,contrary to mainstream literature on trading time above a certain psychological threshold,the volumes exchanged are not integral agents for VSTPC.Currently,financial markets face many ultrafast orders,yet a coherent theory of price change at time scales incomprehensible by humans and only manageable by computers is still lacking.The theory presented in this paper attempts to fill this gap.The outcome of such a theory is important for purposes of market stability,crisis avoidance,investment planning,risk management,and high-frequency trading.展开更多
基金This research is supported by Supported by the Natural Science Foundation of China under Grant Nos. 10701082 and 70801068, the major program of Key Research Institute of Humanities and Social Sciences at Universities （08JJD790145）, and a grant from the ＂project 211 （Phase III）＂.
文摘This paper considers the problem of minimizing the VaR and CTE of an insurer＇s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, the authors give the explicit reinsurance forms and the minimal VaR and CTE of retained risk in the case of quota-share after stop-loss reinsurance and the case of stop-loss afterquota-share reinsurance respectively. Finally, the authors conclude that the quota-share after stop-loss is a better reinsurance strategy than stop-loss after quota-share to minimize the VaR and CTE with a same constrained reinsurance premium. And the pure stop-loss reinsurance is preferred for an insurer with a high level regulatory requirement.
文摘Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.
基金supported by the National Natural Science Foundation of China(11571198,11701319)
文摘In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.
文摘We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.
文摘Academic research has identified several factors that affect price movements;however,the scenario changes abruptly in the case of very short time price changes(VSTPC).This topic is not specifically examined in the existing literature;nonetheless,the behavior of the market microstructure is quite different at the subsecond scale.Indeed,below a certain psychological time threshold,most factors typically influencing price changes cease to apply.This paper analyzes several parameters considered to affect price changes and identifies four of them as potentially influencing VSTPC.These factors are previous volatility,scarce liquidity,high quantity exchanged,and stop-loss(SL)orders(seldom mentioned in the literature).These four parameters are examined by means of a mathematical model,audit trail data analysis,Granger-causality testing,and agent-based model.The results of these four techniques converge to suggest a nonlinear combination of previous volatility,liquidity,and SL orders as the main causes of excess volatility.However,contrary to mainstream literature on trading time above a certain psychological threshold,the volumes exchanged are not integral agents for VSTPC.Currently,financial markets face many ultrafast orders,yet a coherent theory of price change at time scales incomprehensible by humans and only manageable by computers is still lacking.The theory presented in this paper attempts to fill this gap.The outcome of such a theory is important for purposes of market stability,crisis avoidance,investment planning,risk management,and high-frequency trading.
