This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one...This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.展开更多
In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate o...In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate of convergence of the splitstep q-scheme in strong sense is one half.Some numerical experiments are carried out to assert our theoretical result.展开更多
基金This research is supported by the National Science Foundation for Distinguished Young Scholars under Grant No. 70825002, the National Natural Science Foundation of China under Grant No. 70518001, and the National Basic Research Program of China 973 Program under Grant No. 2007CB814902.
文摘This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.
基金supported by the National Natural Science Foundations of China under grant numbers Nos.11571206,91130003 and 11171189.
文摘In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate of convergence of the splitstep q-scheme in strong sense is one half.Some numerical experiments are carried out to assert our theoretical result.
