Year: 2024
Type: article
Abstract: . This paper investigates the callable convertible bond problem in the presence of a liquidity constraint modeled by Poisson signals. We assume that neither the bondholder nor the firm has absolute priority when they stop the game simultaneously, but instead, a proportion [Formula: see text] of the bond is converted to the firm’s stock and the rest is called by the firm. The paper thus generalizes the special case studied in [G. Liang and H. Sun, SIAM J. Control Optim., 57 (2019), pp. 2962–2991], where the bondholder has priority ([Formula: see text]), and presents a complete solution to the callable convertible bond problem with liquidity constraint. The callable convertible bond is an example of a Dynkin game, but falls outside the standard paradigm since the payoffs do not depend in an ordered way upon which agent stops the game. We show how to deal with this nonordered situation by introducing a new technique which may be of interest in its own right, and then apply it to the bond problem.
DOI: 10.1137/24m1648454
Authors: David Hobson, Gechun Liang, Edward Wang
Institution: University of Warwick
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Awards: G5030336097, G8907144345
OpenAlex ID: W4404723254