The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model

DOI10.2143/AST.38.1.2030402zbMath1169.91390OpenAlexW4235194794MaRDI QIDQ3395759

Yi Lu, Shuanming Li

Publication date: 13 September 2009

Published in: ASTIN Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2143/ast.38.1.2030402

zbMATH Keywords

maximum severity of ruinexpected discounted penalty functiondividends-penalty identityMarkov-modulated risk modelmaximum surplus before ruin

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05)

Related Items (28)

The Gerber-Shiu penalty functions for two classes of renewal risk processes ⋮ Analysis of some ruin-related quantities in a Markov-modulated risk model ⋮ Perturbed MAP Risk Models with Dividend Barrier Strategies ⋮ On a risk model with Markovian arrivals and tax ⋮ Optimal dividend payment strategies with debt constraint in a hybrid regime-switching jump-diffusion model ⋮ Some ruin problems for the MAP risk model ⋮ Numerical method for a Markov-modulated risk model with two-sided jumps ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ The maximum surplus before ruin and related problems in a jump-diffusion renewal risk process ⋮ Joint and supremum distributions in the compound binomial model with Markovian environment ⋮ On the Markov-dependent risk model with tax ⋮ The maximum severity of ruin in a perturbed risk process with Markovian arrivals ⋮ Some state-specific exit probabilities in a Markov-modulated risk model ⋮ The discounted penalty function with multi-layer dividend strategy in the phase-type risk model ⋮ A unified analysis of claim costs up to ruin in a Markovian arrival risk model ⋮ A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model ⋮ A matrix operator approach to a risk model with two classes of claims ⋮ Total duration of negative surplus for an MAP risk model ⋮ On the Markov-modulated insurance risk model with tax ⋮ When does surplus reach a given target before ruin in the Markov-modulated diffusion model? ⋮ The Markovian regime-switching risk model with a threshold dividend strategy ⋮ A note on a generalized discounted penalty function in a Sparre Andersen risk model perturbed by diffusion ⋮ A Markov Additive Risk Process with a Dividend Barrier ⋮ “The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model,” Jiandong Ren, July 2007 ⋮ The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model ⋮ Strategies for Dividend Distribution: A Review ⋮ Analysis of a Generalized Penalty Function in a Semi-Markovian Risk Model ⋮ Gerber-Shiu analysis of a risk model with capital injections

Cites Work

• On the joint distribution of surplus before and after ruin under a Markovian regime switching model
• A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier
• Bounds for the ruin probability under a markovian modulated risk model
• The Time Value of Ruin in a Sparre Andersen Model

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