Present value distributions with applications to ruin theory and stochastic equations

DOI10.1016/S0304-4149(97)00072-0zbMath0943.60098MaRDI QIDQ1965872

Håkon K. Gjessing, Jostein Paulsen

Publication date: 1 March 2000

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Laplace transformcharacteristic functionintegro-differential equationstochastic equationruin probabilitypresent value distribution

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Implicit renewal theory and tails of solutions of random equations
• Explicit stationary distributions for compositions of random functions and products of random matrices
• Ruin problems with compounding assets
• Ruin problems with assets and liabilities of diffusion type
• On the stochastic equation \({\mathcal L}(X)={\mathcal L}[B(X+C)\) and a property of gamma distributions]
• On the distribution of a randomly discounted compound Poisson process
• Risk theory in a stochastic economic environment
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
• On some exponential functionals of Brownian motion
• Present value of some insurance portfolios

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