A unique solution to a semilinear Black-Scholes partial differential equation for valuing multi-assets of American options

In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.

The recommendations of Chinese Parkinson’s disease and movement disorder society consensus on therapeutic management of Parkinson’s disease

Background:Parkinson’s disease(PD)is a chronic,progressive and debilitating disease,which affects over 2.5 million people in China.PD is characterized clinically by resting tremor,muscular rigidity,bradykinesia and postural instability.As the disease progresses,additional complications can arise such as non-motor and neurobehavioral symptoms.Pharmacological treatment and surgical intervention for PD have been implemented in China.Until 10 years ago,there was lack of standardization for the management of PD in different regions and among different physicians,leading to different treatment levels in different regions and different physicians.Since then,the Chinese Parkinson’s Disease and Movement Disorder Society have published three versions of guidelines for the management of PD in China,in 2006,2009 and 2014,respectively.Correspondingly,the overall level of treatment for PD in China improved.Objectives:To update the treatment guidelines based on current foreign and domestic practice guidelines and clinical evidence,and to improve the treatment options available to physicians in the management of PD.Summary:A variety of treatment recommendations in the treatment guidelines have been proposed,including physical activity and disease-modifying medication,which should be initiated at the early-stage of the disease.The principles of dosage titration should be followed to avoid acute adverse reactions to the drugs,to achieve a satisfactory clinical effect with a low dose and to reduce the incidence of long-term motor complications.Moreover,different treatment strategies should be considered at different stages of the disease.Importantly,treatment guidelines and personalized treatments should be valued equally.A set of treatment recommendations has been developed to assist physicians to improve and optimize clinical outcomes for patients with PD in China.

PRICING FOR CORPORATE PROPERTY RIGHTS TRANSFER WITH STOCHASTIC MARKETS

This paper employs the real option theory to develop a pricing model for the transfer of property rights.We list the conditions for the good,intermediate and bad firms respectively,and work out the closed-form solution to the equilibrium transfer price,the optimal transfer timing.Using the comparative static analysis,we find that for good firms the transfer price of the target is increasing in its capital.The higher the capital of the target owns,the faster it will be transferred.For intermediate and bad firms,similar conclusions can be derived.The larger gap between the acquirer＇s size and market power and those of the target,the lower the transfer triggered price.The transfer price goes up as the capital ratio of the acquirer over the target diminishes,while it is decreasing in the amount of the capital the target owns.