Multi-utility representations of incomplete preferences induced by set-valued risk measures

不完全市场下$g$-期望效用与一般约束下的最优投资与消费

Optimal investment and consumption under $g$- expected utility and general constraints in incomplete market

本文研究不完全市场中非线性期望与一般约束下的效用最大化问题，利用$g$-鞅方法为不同效用函数求得显式解，并通过二次BSDE刻画最优投资-消费策略。

Robust no arbitrage and the solvability of vector-valued utility maximization problems

A market model with $d$ assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a numèraire is not assumed. It is shown that robust no arbitrage holds if, and only if, there exists a Pareto solution for some vector-valued utility maximization problem with component-wise utility functions. Moreover, it is demonstrated that a consistent price process can be constructed from the Pareto maximizer.

Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and se…

Incomplete stochastic equilibria for dynamic monetary utility

We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete market model among a group of agents whose preference is characterized by cash invariant time-consistent monetary utilities. An assumption of "smallness" type is shown to be sufficient for existence and uniqueness. In particular, this assumption encapsulates settings with small endowments, small time-horizon, or a large population of weakly heterogeneous agents. Central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.

不完备市场中衍生品证券的最优头寸配置

Optimal positioning in derivative securities in incomplete markets

本文研究不完备市场中基于单一标的普通期权的两资产静态对冲问题，将其建模为效用最大化，并给出多种效用下的半解析解及 Lipschitz 不动点收敛结论。

对数效用与不确定性模型下的最优投资与消费

Optimal investment and consumption under logarithmic utility and uncertainty model

针对不完全市场中带一般非凸随机约束的对数效用鲁棒最大化问题，将其转化为非线性期望对数效用最大化，并用二次 BSDE 刻画最优解。