Kalman-Bucy Filtering for Linear Systems Driven by the Cox Process with Shot Noise Intensity and Its Application to the Pricing of Reinsurance Contracts

DOI10.1239/jap/1110381373zbMath1076.62093OpenAlexW2020850534MaRDI QIDQ5312843

Angelos Dassios, Ji-Wook Jang

Publication date: 25 August 2005

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1110381373

zbMATH Keywords

Gaussian processCox processshot noise processstop-loss reinsurance contractKalman--Bucy filterpiecewise-deterministic Markov process theory

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Central limit and other weak theorems (60F05) Signal detection and filtering (aspects of stochastic processes) (60G35) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (17)

Approximation for portfolio optimization in a financial market with shot-noise jumps ⋮ A micro-level claim count model with overdispersion and reporting delays ⋮ Lapse risk in life insurance: correlation and contagion effects among policyholders' behaviors ⋮ A dynamic contagion process ⋮ Moments of renewal shot-noise processes and their applications ⋮ Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process ⋮ Ruin probabilities in a Markovian shot-noise environment ⋮ A risk model with renewal shot-noise Cox process ⋮ Optimal reinsurance via BSDEs in a partially observable model with jump clusters ⋮ Optimal proportional reinsurance to maximize an insurer’s exponential utility under unobservable drift ⋮ Mean-variance portfolio selection for a non-life insurance company ⋮ Some limit results on the Haar-Fisz transform for inhomogeneous Poisson signals ⋮ A Markov modulated dynamic contagion process with application to credit risk ⋮ Risk processes with shot noise Cox claim number process and reserve dependent premium rate ⋮ Particle Filters for Partially Observed Diffusions ⋮ Shot noise, weak convergence and diffusion approximations ⋮ Ruin probabilities and aggregrate claims distributions for shot noise Cox processes

Cites Work

• On Cox processes and credit risky securities
• Aspects of risk theory
• Doubly stochastic Poisson processes
• Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity
• Explosive Poisson shot noise processes with applications to risk reserves
• The virtual waiting-time and related processes
• Martingales and insurance risk
• Generalized Poisson Models and their Applications in Insurance and Finance
• Conditional Poisson processes
• Stochastic differential equations. An introduction with applications.
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