In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Li...In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Lipschtz assumptions.展开更多
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal ...This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.展开更多
文摘In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Lipschtz assumptions.
基金supported by National Natural Science Foundation of China(Grant Nos.11271143,11371155 and 11326199)University Special Research Fund for Ph D Program(Grant No.20124407110001)+1 种基金National Natural Science Foundation of Zhejiang Province(Grant No.Y6110775)the Oxford-Man Institute of Quantitative Finance
文摘This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.
