Perpetual convertible bonds in jump-diffusion models

Abstract

Statistics and Decisions (2005) 23(1) (15-31) AbstractA convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give an explicit solution to the corresponding optimal stopping game in the context of a reduced form model driven by a Brownian motion and a compound Poisson process with exponential jumps. It turns out that the occurrence of jumps leads to optimal stopping strategies whose structure differs from the results for continuous models.

Nonzero-Sum Games of Optimal Stopping for Markov Processes

“…For further details one can refer to [39] and the references therein. Zero-sum optimal stopping games have been used extensively in the pricing of game contingent claims both in complete and incomplete markets (see for example [15,17,24,25,30,33,35,36,38] and [19]). …”

Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes

“…Such a model was considered in [20]- [21], [17]- [19] and [12]- [13], where some one-dimensional optimal stopping problems were solved. We note that the chosen approach based on reducing the initial optimal stopping problem to solving the associated free-boundary problem provides more valuable information on the nature of the solution and its analytic properties than the standard so-called guess-and-verify approach.…”

Further Calculations for the McKean Stochastic Game for a Spectrally Negative Lévy Process: From a Point to an Interval

“…For other examples of stochastic games, see e.g. Kifer [12], Kyprianou [14], Baurdoux and Kyprianou [3], Gapeev and Kühn [10], Baurdoux et al [4]. Note that the McKean game can be seen as an extension of the classic McKean optimal stopping problem (cf.…”