BOUNDS ON OPTION PRICES IN POINT PROCESS DIFFUSION MODELS

We obtain lower and upper bounds on option prices in one-dimensional jump-diffusion markets with point process components. Our proofs rely in general on the classical Kolmogorov equation argument and on the propagation of convexity property for Markov semigroups, but the bounds on intensities and jump sizes formulated in our hypotheses are different from the ones already found in the literature (Finance and Stochastics4(2) (2000) 209–222; 10(2) (2006) 229–249).

On Threshold Strategies and the Smooth-Fit Principle for Optimal Stopping Problems

In this paper we investigate sufficient conditions that ensure the optimality of threshold strategies for optimal stopping problems with finite or perpetual maturities. Our result is based on a local-time argument that enables us to give an alternative proof of the smooth-fit principle. Moreover, we present a class of optimal stopping problems for which the propagation of convexity fails.

On Threshold Strategies and the Smooth-Fit Principle for Optimal Stopping Problems

In this paper we investigate sufficient conditions that ensure the optimality of threshold strategies for optimal stopping problems with finite or perpetual maturities. Our result is based on a local-time argument that enables us to give an alternative proof of the smooth-fit principle. Moreover, we present a class of optimal stopping problems for which the propagation of convexity fails.