Continuous-time limits of multi-period cost-of-capital margins

Engsner Hampus () and Lindskog Filip ()
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Engsner Hampus: Department of Mathematics, Stockholm University, Stockholm, Sweden
Lindskog Filip: Department of Mathematics, Stockholm University, Stockholm, Sweden

Statistics & Risk Modeling, 2020, vol. 37, issue 3-4, 79-106

Abstract: We consider multi-period cost-of-capital valuation of a liability cash flow subject to repeated capital requirements that are partly financed by capital injections from capital providers with limited liability. Limited liability means that, in any given period, the capital provider is not liable for further payment in the event that the capital provided at the beginning of the period turns out to be insufficient to cover both the current-period payments and the updated value of the remaining cash flow. The liability cash flow is modeled as a continuous-time stochastic process on [ 0 , T ] {[0,T]} . The multi-period structure is given by a partition of [ 0 , T ] {[0,T]} into subintervals, and on the corresponding finite set of times, a discrete-time cost-of-capital-margin process is defined. Our main objective is the analysis of existence and properties of continuous-time limits of discrete-time cost-of-capital-margin processes corresponding to a sequence of partitions whose meshes tend to zero. Moreover, we provide explicit expressions for the limit processes when cash flows are given by Itô diffusions and processes with independent increments.

Keywords: Multi-period valuation; cost-of-capital margin; continuous-time limit (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/strm-2019-0008

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