Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

FASL polymorphism is associated with response to bacillus Calmette-Guérin immunotherapy in bladder cancer

Objective Deregulation of FAS/FASL system may lead to immune escape and influence bacillus Calmette-Guérin (BCG) immunotherapy outcome, which is currently the gold standard adjuvant treatment for high-risk non–muscle invasive bladder tumors. Among other events, functional promoter polymorphisms of FAS and FASL genes may alter their transcriptional activity. Therefore, we aim to evaluate the role of FAS and FASL polymorphisms in the context of BCG therapy, envisaging the validation of these biomarkers to predict response. Patients and methods DNA extracted from peripheral blood from 125 patients with bladder cancer treated with BCG therapy was analyzed by Polymerase Chain Reaction—Restriction Fragment Length Polymorphism for FAS-670 A/G and FASL-844 T/C polymorphisms. FASL mRNA expression was analyzed by real-time Polymerase Chain Reaction. Results Carriers of FASL-844 CC genotype present a decreased recurrence-free survival after BCG treatment when compared with FASL-844 T allele carriers (mean 71.5 vs. 97.8 months, P = 0.030) and have an increased risk of BCG treatment failure (Hazard Ratio = 1.922; 95% Confidence Interval: [1.064–3.471]; P = 0.030). Multivariate analysis shows that FASL-844 T/C and therapeutics scheme are independent predictive markers of recurrence after treatment. The evaluation of FASL gene mRNA levels demonstrated that patients carrying FASL-844 CC genotype had higher FASL expression in bladder tumors (P = 0.0027). Higher FASL levels were also associated with an increased risk of recurrence after BCG treatment (Hazard Ratio = 2.833; 95% Confidence Interval: [1.012–7.929]; P = 0.047). FAS-670 A/G polymorphism analysis did not reveal any association with BCG therapy outcome. Conclusions Our results suggest that analysis of FASL-844 T/C, but not FAS-670 A/G polymorphisms, may be used as a predictive marker of response to BCG immunotherapy.