Stochastic differential equations for compounded risk reserves

DOI10.1016/0167-6687(89)90054-1zbMath0688.62056OpenAlexW2006715347WikidataQ126781787 ScholiaQ126781787MaRDI QIDQ1263913

K. Appert

Publication date: 1989

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6687(89)90054-1

zbMATH Keywords

Brownian motioninflationdiscountingstopping timesdiffusion modelsruin probabilitiesdividend paymentsdistribution of time to ruininvestment incomeperturbed processesrisk reserves

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items

The First-passage Time of the Brownian Motion to a Curved Boundary: an Algorithmic Approach, Crossing probabilities for diffusion processes with piecewise continuous boundaries, A theory of risk, return and solvency, On the generalized Gerber-Shiu function for surplus processes with interest, On reinsurance and investment for large insurance portfolios, CONDITIONAL RUIN PROBABILITY WITH STOCHASTIC INTEREST RATE, On absolute ruin minimization under a diffusion approximation model, Premium and reinsurance control of an ordinary insurance system with liabilities driven by a fractional Brownian motion, Optimal proportional reinsurance policies for stochastic models, Ruin problems with assets and liabilities of diffusion type, Ruin Minimization for Insurers with Borrowing Constraints

Cites Work

• Unnamed Item
• Unnamed Item
• Estimates for the probability of ruin starting with a large initial reserve
• Diffusion premiums for claim severities subject to inflation
• Ruin problems with compounding assets
• On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures
• Macro-economic influences on the crossing of dividend barriers
• Gaussian-Markov Processes and a Boundary Value Problem
• Explicit Solutions to Some Problems of Optimal Stopping
• Diffusion approximations in collective risk theory
• The First Passage Problem for a Continuous Markov Process