Real-option valuation in multiple dimensions using Poisson optional stopping times

We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process; this can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation and broadly applicable in analyzing multidimensional option-valuation problems.University of Cambridge Judge Business School small research grant 201

Progression-free survival versus post-progression survival and overall survival in WHO grade 2 gliomas

Background and purpose: Progression-free survival (PFS) remains to be validated as an outcome measure for diffuse WHO grade 2 gliomas, and knowledge about the relationships between PFS, post-progression survival (PPS), and overall survival (OS) in this subset of tumors is limited. We sought to assess correlations between PFS and OS, and identify factors associated with PFS, PPS, and OS in patients treated for diffuse supratentorial WHO grade 2 gliomas. Material and methods: We included 319 patients from three independent observational cohorts. The correlation between PFS and OS was analyzed using independent exponential distributions for PFS and time from progression to death. Cox proportional hazards models were used to determine the effects of covariates on PFS, PPS, and OS. Results: The overall correlation between PFS and OS was rs0.31. The correlation was rs 0.37 for astrocytomas and rs 0.19 for oligodendrogliomas. Longer PFS did not predict longer PPS. Patients with astrocytomas had shorter PFS, PPS, and OS. Larger preoperative tumor volume was a risk factor for shorter PFS, while older age was a risk factor for shorter PPS and OS. Patients who received early radio- and chemotherapy had longer PFS, but shorter PPS and OS. Interpretation: We found a weak correlation between PFS and OS in WHO grade 2 gliomas, with the weakest correlation observed in oligodendrogliomas. Our analyses did not demonstrate any association between PFS and PPS. Critically, predictors of PFS are not necessarily predictors of OS. There is a need for validation of PFS as an endpoint in diffuse WHO grade 2 gliomas.publishedVersio