The present value of a perpetuity with stochastic discounting
Lindblad, Jonas (2019)
Lindblad, Jonas
Åbo Akademi
2019
Julkaisu on tekijänoikeussäännösten alainen. Teosta voi lukea ja tulostaa henkilökohtaista käyttöä varten. Käyttö kaupallisiin tarkoituksiin on kielletty.
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2019092529843
https://urn.fi/URN:NBN:fi-fe2019092529843
Tiivistelmä
Simple market models typically include a constant rate of risk-free interest, simplifying present value calculations and asset pricing significantly. In this thesis, present value calculations with a stochastic rate of interest is treated for random cash flows, annuities, and in particular, perpetuities. The literature on the finiteness and central moments of the present value of a perpetual cash flow is discussed and higher-order moment formulas are derived for several special cases, in particular for a continuous finite or infinite constant cash flow subject to an interest rate given by a Lévy process. The main part of the work is a long list of cases, some being new, when the density of the present value of a perpetuity can be found or a simple expression in terms of independent stochastic variables can be derived. Applications to stock valuation, approximation methodology, and risk theory are discussed briefly at the end.
Kokoelmat
- 111 Matematiikka [37]