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Risk Models and Ruin Theory

Hanji Shang

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Abstract

AbstractThe following sections are included:On the Distribution of Surplus Immediately after Ruin under Interest ForceThe Risk ModelEquations for ${\mathop G\limits^=}_ \delta (u, y)$Integral Equations for ${\mathop G\limits^=}_ \delta (u, y)$, Ḡδ(u, y) and Gδ(u, y)The Case δ = 0Upper and Lower Bounds for Ḡδ(0, y)On the Distribution of Surplus Immediately before Ruin under Interest ForceEquations for Bδ(u, y)Integral Equations for Bδ(u, y)The Case δ = 0Solution of the Integral EquationBδ(u, y) with Zero Initial ReserveExponential Claim SizeLundberg BoundAsymptotic Estimates of the Low and Upper Bounds for the Distribution of the Surplus Immediately after Ruin under Subexponential ClaimsPreliminaries and Auxiliary RelationsAsymptotic Estimates of the Low and Upper BoundsOn the Ruin Probability under a Class of Risk ProcessesThe Risk ModelThe Laplace Transform of the Ruin Probability with Finite TimeTwo CorollariesReferences

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AbstractThe following sections are included:On the Distribution of Surplus Immediately after Ruin under Interest ForceThe Risk ModelEquations for ${\mathop G\limits^=}_ \delta (u, y)$Integral Equations for ${\mathop G\limits^=}_ \delta (u, y)$, Ḡδ(u, y) and Gδ(u, y)The Case δ = 0Upper and Lower Bounds for Ḡδ(0, y)On the Distribution of Surplus Immediately before Ruin under Interest ForceEquations for Bδ(u, y)Integral Equations for Bδ(u, y)The Case δ = 0Solution of the Integral EquationBδ(u, y) with Zero Initial ReserveExponential Claim SizeLundberg BoundAsymptotic Estimates of the Low and Upper Bounds for the Distribution of the Surplus Immediately after Ruin under Subexponential ClaimsPreliminaries and Auxiliary RelationsAsymptotic Estimates of the Low and Upper BoundsOn the Ruin Probability under a Class of Risk ProcessesThe Risk ModelThe Laplace Transform of the Ruin Probability with Finite TimeTwo CorollariesReferences

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Available abstract

AbstractThe following sections are included:On the Distribution of Surplus Immediately after Ruin under Interest ForceThe Risk ModelEquations for ${\mathop G\limits^=}_ \delta (u, y)$Integral Equations for ${\mathop G\limits^=}_ \delta (u, y)$, Ḡδ(u, y) and Gδ(u, y)The Case δ = 0Upper and Lower Bounds for Ḡδ(0, y)On the Distribution of Surplus Immediately before Ruin under Interest ForceEquations for Bδ(u, y)Integral Equations for Bδ(u, y)The Case δ = 0Solution of the Integral EquationBδ(u, y) with Zero Initial ReserveExponential Claim SizeLundberg BoundAsymptotic Estimates of the Low and Upper Bounds for the Distribution of the Surplus Immediately after Ruin under Subexponential ClaimsPreliminaries and Auxiliary RelationsAsymptotic Estimates of the Low and Upper BoundsOn the Ruin Probability under a Class of Risk ProcessesThe Risk ModelThe Laplace Transform of the Ruin Probability with Finite TimeTwo CorollariesReferences

Key concepts: Ruin theory, History, Risk model, Mathematical economics, Economics

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