The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study...The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.展开更多
In this note, we give a necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of Rm. Our result is the system is viable in a closed submanifold K iff the co...In this note, we give a necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of Rm. Our result is the system is viable in a closed submanifold K iff the coefficients are tangent to K along K if the equation is in the sense of stratonovich integral and the solution jumps from K to K.展开更多
Objective To study the mechanism of myocardial dielectric property changes in radio frequency during hypothermic preservation and explore myocardial viability evaluative method. Methods Hybrid young pigs ( 20 - 30 kg)...Objective To study the mechanism of myocardial dielectric property changes in radio frequency during hypothermic preservation and explore myocardial viability evaluative method. Methods Hybrid young pigs ( 20 - 30 kg) were used in the experiment. Heart arrest was in-展开更多
This paper investigates some important properties of Z, the martingale integrant of the backward stochastic differential equations, which is the second process of the solution. These include the backward stochastic vi...This paper investigates some important properties of Z, the martingale integrant of the backward stochastic differential equations, which is the second process of the solution. These include the backward stochastic viability property, bounded property and the comparison theorem. To explain the theoretical results, the authors apply them to study a financial contingent claim pricing problem. The replication portfolio process can be characterized clearly.展开更多
In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation （BSDE） when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrag...In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation （BSDE） when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrage financial market. Furthermore, motivated by the behavior of agents in finance market, we introduce a new total order q on Rn and obtain a necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order. We also give some further results for q展开更多
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA079,ZR2021MG049)the National Social Science Funding of China(Grant No.21CJY027).
文摘The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.
基金Supported by"the Fundamental Research Funds for the Central Universities"(No.3082015NZ2015111)
文摘In this note, we give a necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of Rm. Our result is the system is viable in a closed submanifold K iff the coefficients are tangent to K along K if the equation is in the sense of stratonovich integral and the solution jumps from K to K.
文摘Objective To study the mechanism of myocardial dielectric property changes in radio frequency during hypothermic preservation and explore myocardial viability evaluative method. Methods Hybrid young pigs ( 20 - 30 kg) were used in the experiment. Heart arrest was in-
基金supported by the National Natural Science Foundation of China under Grant Nos.10921101, 61174092,11026185 and 11101242the National Science Foundation for Distinguished Young Scholars of China under Grant No.11125102+1 种基金the Natural Science Foundation of Shandong Province,China under Grant No.ZR2010AQ004the Independent Innovation Foundation of Shandong University under Grant No. 2009TS036
文摘This paper investigates some important properties of Z, the martingale integrant of the backward stochastic differential equations, which is the second process of the solution. These include the backward stochastic viability property, bounded property and the comparison theorem. To explain the theoretical results, the authors apply them to study a financial contingent claim pricing problem. The replication portfolio process can be characterized clearly.
基金Supported partly by the National Science Foundation of China(Grant No.11231005)the China Postdoctoral Science Foundation(Grant No.2013M541899)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2013AQ021)
文摘In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation （BSDE） when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrage financial market. Furthermore, motivated by the behavior of agents in finance market, we introduce a new total order q on Rn and obtain a necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order. We also give some further results for q
