This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables,the author obtains a strong law of large numbers under...This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables,the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.展开更多
This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state con...This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland＇s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11501325,11231005)
文摘This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables,the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.
基金supported by the National Natural Science Foundation of China under Grant No.11171076Science and Technology Commission,Shanghai Municipality under Grant No.14XD1400400
文摘This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland＇s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.
