A Bayesian approach for optimal reinsurance and investment in a diffusion model

A Bayesian adaptive control approach to the combined optimal investment/reinsurance problem of an insurance company is studied. The insurance company invests in a money market and a capital market index with an unknown appreciation rate, or “drift”. Using a Bayesian approach, the unknown drift is described by an unobservable random variable with a known (prior) probability distribution. We assume that the risk process of the company is governed by a diffusion approximation to the compound Poisson risk process. The company also purchases reinsurance. The combined optimal investment/reinsurance problem is formulated as a stochastic optimal control problem with partial observations. We employ filtering theory to transform the problem into one with complete observations. The control problem is then solved by the dynamic programming Hamilton–Jacobi–Bellman (HJB) approach. Semi-analytical solutions are obtained for the exponential utility case.Xin Zhang; Robert J. Elliott; Tak Kuen Si

Prognostic significance of whole-body MRI in patients with monoclonal gammopathy of undetermined significance

Radiological skeletal survey or computed tomography are currently applied to assess bone diseases in patients with monoclonal plasma cell disorders. Whole-body magnetic resonance imaging (whole-body MRI) allows detecting the infiltration of clonal cells in nearly the whole bone marrow compartment even before bone destruction has occurred. Those MRI results (i.e., patterns of bone marrow infiltration) have been demonstrated to be of prognostic significance in patients with symptomatic as well as asymptomatic multiple myeloma. We have therefore analyzed the findings of whole-body MRI in 137 consecutive individuals with monoclonal gammopathy of undetermined significance (MGUS). A focal infiltration pattern was detected in 23.4% of patients. Presence and number of focal lesions as well as value of M-Protein were of independent prognostic significance for progression into a symptomatic disease requiring systemic treatment (P=0.02; P<0.0001 and P=0.0005, respectively). Lower homogeneous signal intensities in T1-weighted images were related to a physiologically higher bone marrow cellularity in younger individuals (P=0.002). We conclude that whole-body MRI identifies patients with focal accumulations of presumably monoclonal cells in bone marrow with prognostic impact concerning the risk of progression into symptomatic disease