Please use this identifier to cite or link to this item:
Title: Dam rain and cumulative gain
Authors: Brody, DC
Hughston, LP
Macrina, A
Keywords: Asset pricing;Insurance claim reserves;Credit portfolio risk;Gamma bridge process;Beta distribution;Reinsurance
Issue Date: 2008
Publisher: The Royal Society
Citation: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 464(2095), 1801 - 1822, 2008
Abstract: We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting, aggregate claims play the role of cumulative gains, and the terminal cash flow represents the totality of the claims payable for the given accounting period. A similar example arises when we consider the accumulation of losses in a credit portfolio, and value a contract that pays an amount equal to the totality of the losses over a given time interval. An expression for the value process of such an asset is derived as follows. We fix a probability space, together with a pricing measure, and model the terminal cash flow by a random variable; next, we model the cumulative gains process by the product of the terminal cash flow and an independent gamma bridge; finally, we take the filtration to be that generated by the cumulative gains process. An explicit expression for the value process is obtained by taking the discounted expectation of the future cash flow, conditional on the relevant market information. The price of an Arrow–Debreu security on the cumulative gains process is determined, and is used to obtain a closed-form expression for the price of a European-style option on the value of the asset at the given intermediate time. The results obtained make use of remarkable properties of the gamma bridge process, and are applicable to a wide variety of financial products based on cumulative gains processes such as aggregate claims, credit portfolio losses, defined benefit pension schemes, emissions and rainfall.
Description: This article is available open access through the publisher’s website at the link below. Copyright @ 2008 The Royal Society.
ISSN: 1364-5021
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

Files in This Item:
File Description SizeFormat 
Notice.pdf41.15 kBAdobe PDFView/Open

Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.