The Random Walk of a Simple Risk Business
H. L. Seal
ASTIN Bulletin, 1966, vol. 4, issue 1, 19-28
Abstract:
We suppose that a risk business issues a single type of contract under which, in return for a unit “premium”, it will pay a “sum insured” m (m being an integer) on the occurrence of a contingency of probability q ˂ ½. The expected gain on each contract is i—mq and is assumed to be positive. This type of enterprise is conveniently denominated a simple risk business. Two “real life” situations it simulates are those of a group life policy for a uniform amount covering a number of young lives (e.g., university students), and a roulette casino where the stakes are uniform and the bets are limited to the single numbers o to 36.The risk business is supposed to commence its operations with a “risk reserve” of K units. Each premium is added to this reserve as it is received and all claims by contract holders are paid there-from. We say that the business is “ruined” as soon as the risk reserve becomes zero or negative (though it could be argued that it would be unethical to accept a premium once the risk reserve is less than m — 1). On the other hand, if the reserve reaches an amount M units no further premiums are paid into it until a claim occurs to reduce it below M (de Finetti, 1957). The risk business intends to continue its operations for a long, but finite, period unless ruined in the meantime.We consider two probabilities: (i) υx, the chance of eventual ruin given that the risk reserve is now x, and (ii) υx, n, the probability that ruin occurs as a result of the nth contract (simultaneous contracts being ranked in a prearranged, e.g., alphabetical, order). Clearly and we will write I — νx=μx
Date: 1966
References: Add references at CitEc
Citations:
Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:cup:astinb:v:4:y:1966:i:01:p:19-28_00
Access Statistics for this article
More articles in ASTIN Bulletin from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().