Maximum principle for a Markovian regime switching system under model uncertainty

In this paper, we study a stochastic optimal control problem with a Markovian regime switching system, where the coefficients of the state equation and the cost functional are uncertain. First, we obtain the variational inequality by showing the continuity with respect to the uncertainty parameter of the variational equation, which is characterized as forward-backward stochastic differential equations. Second, using the linearization method and weak convergence technique, we prove the necessary stochastic maximum principle and show the sufficient condition of the stochastic optimal control. Finally, as an application, a risk-minimizing portfolio selection problem is studied. Meanwhile, the $L^\beta$-solution and $L^\beta$-estimate of stochastic differential equations with regime switching are given for \b=2k with $k\in \mathbb{N}$.Comment: 37 Page

COMPATIBILITY EVALUATION OF BZ25-1 CRUDE OILS IN BOHAI BAY, CHINA

ABSTRACT BZ25-1 oilfield is located in the southeast of Bohai bay which geographically lies between 119 o 00′to 119 o 15′east longitude and 38 o 10′to 38 o 20′north latitude. It has two oil blocks, including Shahejie (SHJ) waxy oil and Minghuazhen (MHZ) heavy oil, with six wellhead platforms WHPA~WHPF and six submarine pipelines. Therein, the WHPC-WHPB and WHPB-SPM (Single Point Mooring) pipelines transport the mixture of the two produced crude oils. However, the mixing of the two oils will certainly bring out a change in their components and properties, which directly affects the safe operation of the submarine pipelines and offshore production facilities. Therefore, this paper compounds three kinds of MHZ/SHJ mixed oils with blending ratios of 1:1, 3:1 and 9:1, mainly studies how the components, rheological and thermophysical properties of the oil mixtures change with the blending ratio. The major objective of this study is to evaluate the compatibility of the two crude oils and provide a theoretical basis for the production optimization and risk elusion of the oilfield. The results of the study show that the components and properties of SHJ crude oil are quite different from those of MHZ oil, the flow behavior of SHJ oil is more sensitive to temperature. As MHZ oil in the compounds increases, the contents of asphaltene, resin, sulfur and carbon residue will increase except wax contents, their viscosities, densities and flash points will also increase, but their pour points, yield stresses, calorific values and other major thermophysical parameters will decrease. A blending ratio of 2~7:1 for MHZ to SHJ crude oil can be concluded to make the properties of the compounds meet the safe and economic requirements of the subsea pipeline and offshore facility operations and ensure the compatibility of the mixed oils. In actuality, the field operations have confirmed that the recommended blending ratio is reasonable and practicable

Uptake of maternal care and childhood immunization among ethnic minority and Han populations in Sichuan province: a study based on the 2003, 2008 and 2013 health service surveys.

BACKGROUND: China has made remarkable progress in maternal and child health (MCH) over the last thirty years, but socio-economic inequalities persist. Ethnicity has become an important determinant of poor MCH outcomes, but little rigorous analytical work has been done in this area. To understand the socio-economic factors that explain ethnic variation in uptake of MCH care, we report the findings from an analysis in Sichuan province. METHODS: We linked data from the 2003, 2008 and 2013 National Health Service Surveys in Sichuan Province. The ethnic disparities in uptake of maternal care (completing 5 antenatal visits, giving birth in hospital and receiving a caesarean section) and childhood immunization (Bacillus Calmette Guerin (BCG), three doses of diphtheria (DPT) and measles immunization) were examined by geographical (Han district/county vs. ethnic minority county) and individual-based (Han women/children vs. ethnic minority women/children) comparisons. We also examined variation by distance to township and county hospitals, women's education, parity and age using weighted multilevel Poisson regressions with random intercept at district/county level. RESULTS: Ethnic inequalities in maternal care were marked, both at the geographical (district/county) and the individual level. The % of births in hospital was 90.7% among women in Han districts, compared to 83.3% among women living in Han counties (crude RR 0.93; 95% CI 0.75-1.15), 53.8% among Han women living in ethnic minority counties (crude RR 0.57; 95% CI 0.36-0.93), and 13.5% among ethnic minority women living in ethnic minority counties (crude RR 0.18; 95% CI 0.06-0.57). Adjusting the analysis for survey year, education, parity and distance to county level hospital weakened the association between geographical/individual ethnicity and uptake of maternity care, but associations remained remarkably strong. Coverage of childhood immunization was much higher than uptake of maternity care, and inequalities by ethnicity were much less pronounced. CONCLUSION: Lessons can be learned from China's successful immunization programme to further reduce inequalities in access to maternity care among ethnic minority populations in remote areas. Bringing the services closer to the women's homes and strengthening health promotion from the township to the village level may encourage more women to seek antenatal care and give birth in hospital

Backward doubly stochastic differential equations and SPDEs with quadratic growth

In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator $f(t,Y,Z)$ grows in $Z$ quadratically and the terminal value is bounded, by introducing some new ideas. Moreover, in this framework, we use BDSDEs to give a probabilistic representation for the solutions of semilinear stochastic partial differential equations (SPDEs, for short) in Sobolev spaces, and use it to prove the existence and uniqueness of such SPDEs, thus extending the nonlinear Feynman-Kac formula.Comment: 43 page

General indefinite backward stochastic linear-quadratic optimal control problems

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite, and the cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly

A sliding window method for detecting corners of openings from terrestrial lidar data

10.5194/isprs-archives-XLII-4-W10-97-2018Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.XLII-4/W1097-10

Stochastic Linear Quadratic Optimal Control Problems with Random Coefficients and Markovian Regime Switching System

This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random. We prove the solvability of the stochastic Riccati equation under the uniform convexity condition and obtain the closed-loop representation of the open-loop optimal control using the unique solvability of the corresponding stochastic Riccati equation. Moreover, by applying It\^{o}'s formula with jumps, we get a representation of the cost functional on a Hilbert space, characterized as the adapted solutions of some forward-backward stochastic differential equations. We show that the necessary condition of the open-loop optimal control is the convexity of the cost functional, and the sufficient condition of the open-loop optimal control is the uniform convexity of the cost functional. In addition, we study the properties of the stochastic value flow of the stochastic linear-quadratic optimal control problem. Finally, as an application, we present a continuous-time mean-variance portfolio selection problem and prove its unique solvability.Comment: 30 pages. arXiv admin note: text overlap with arXiv:1809.0026