Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intrapersonal conflict but unable to commit herself in the future to...

We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses. We also study the utility process in this generalized model with constant elasticity of intertemporal substitution and relative risk aversion degree, and...

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem...

We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency...

In a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature, referred to as weak equilibrium, is not fully aligned with the standard definition of equilibrium in the game theory in that the agent may be willing to deviate from a...

In this paper, we study a portfolio selection problem in which an agent trades a risk-free asset and multiple risky assets with deterministic mean return rates and volatility and wants to maximize the alpha-quantile of her wealth at some terminal time. Because of the time inconsistency caused by...

Risk measures are used not only for financial institutions’ internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk...

In this paper we analyze how changes in inverse S-shaped probability weighting influence optimal portfolio choice in a rank-dependent utility model. We derive sufficient conditions for the existence of an optimal solution of the investment problem, and then define the notion of a more inverse...

We consider the problem of finding the best time to stop a diffusion process for an agent with a preference model that is a mixture of expected utility theory (EUT) and cumulative prospect theory (CPT). In view of time-inconsistency, we consider two types of agent: a naive agent, who is not...

This document contains supplementary materials to "Optimal Exit Time from Casino Gambling: Strategies of Pre-committed and Naive Gamblers" by X.D. He, S. Hu, J. Obloj, and X.Y. Zhou.The paper to which these supplementary materials apply will appear in the SIAM Journal on Control and Optimization...