This paper formulates a model of utility for a continuous time frame-work that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules...

This paper formulates a model of utility for a continuous time framework that captures the decision-maker’s concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a significant departure from existing continuous time...

We formulate a model of utility for a continuous-time framework that captures aversion to ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments....

Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is...

This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a significant departure from existing continuous time...

In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping...

In this paper, we study the pricing of contingent claims under G-expectation. In order to accomodate volatility uncertainty, the price of the risky security is supposed to governed by a general linear stochastic differential equation (SDE) driven by G-Brownian motion. Utilizing the recently...

In this paper, we study a functional fully coupled forward–backward stochastic differential equation (FBSDE). For this functional FBSDE, the classical Lipschitz and monotonicity conditions which guarantee the existence and uniqueness of the solution to FBSDE are no longer applicable. To...

This paper solves an optimal insurance design problem in which both the insurer and the insured are subject to Knightian uncertainty about the loss distribution. The Knightian uncertainty is modeled in a multi-prior g-expectation framework. We obtain an endogenous characterization of the optimal...

In this paper, we study comparison theorem, nonlinear Feynman–Kac formula and Girsanov transformation of the following BSDE driven by a G-Brownian motion: Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt), where K is a decreasing G-martingale.