Reflected forward-backward SDEs and obstacle problems with boundary conditions

In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short). More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem) with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option

Stochastic differential equations driven by fractional Brownian motion and Poisson point process

In this paper, we study a class of stochastic differential equations with additive noise that contains a fractional Brownian motion (fBM) and a Poisson point process of class (QL). The differential equation of this kind is motivated by the reserve processes in a general insurance model, in which the long term dependence between the claim payment and the past history of liability becomes the main focus. We establish some new fractional calculus on the fractional Wiener-Poisson space, from which we define the weak solution of the SDE and prove its existence and uniqueness. Using an extended form of Krylov-type estimate for the combined noise of fBM and compound Poisson, we prove the existence of the strong solution, along the lines of Gy\"{o}ngy and Pardoux (Probab. Theory Related Fields 94 (1993) 413-425). Our result in particular extends the one by Mishura and Nualart (Statist. Probab. Lett. 70 (2004) 253-261).Comment: Published at http://dx.doi.org/10.3150/13-BEJ568 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On Quadratic g-Evaluations/Expectations and Related Analysis

In this paper we extend the notion of g-evaluation, in particular g-expectation, to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a representation theorem between the generator and the corresponding g-expectation, and consequently the reverse comparison theorem of quadratic BSDEs as well as the Jensen inequality, remain true in the quadratic case. Our main results also include a Doob-Meyer type decomposition, the optional sampling theorem, and the up-crossing inequality. The results of this paper are important in the further development of the general quadratic nonlinear expectations.Comment: 27 page

Factors Influencing Productive Activities of the Korean Rural Elderly

The purpose of this study was to identify the factors influencing productive activities of the Korean rural elderly. Utilizing data from the 2004 survey "Living Profile and Welfare Service Needs of Older Persons in Korea," this study predicted the productive activities of the rural elderly. All of the ten predicting variables selected from the survey and literature review (age, gender, education, activity limitation, personal income, health, organization, family status, socio-economic status, and job) were found to have significant partial effects on such productive activities as paid work, care-giving and volunteer work. The following are major conclusions: The rural elderly women had more care-giving, whereas men had more volunteer work. Participation in religious or social organizations was a good predictor for participation in a volunteer work. Single-family status was a negative factor for care-giving. Being a farmer or not could explain the paid working time most effectively. The rural elderly with a relatively high socio-economic status have more inclination to participate in a volunteer work. Aging reduces the possibility of sharing the experiences of paid work or care-giving. Activity limitation had a negative partial effect on care-giving. Good health was the only valuable predictor for all kinds of productive activities. Personal income was positively related with paid work and care-giving. The highly educated were more likely to do unpaid productive work.rural elderly, productive activity, paid work, care-giving, volunteer work, Korea, Agribusiness, Community/Rural/Urban Development, Farm Management, Industrial Organization, Institutional and Behavioral Economics, Labor and Human Capital,