How time-inconsistent preferences influence venture capital exit decisions? A new perspective for grandstanding

Considering that the assumption of time consistency does not adequately reveal the mechanisms of exit decisions of venture capital (VC), this study proposes two kinds of time-inconsistent preferences (i.e., time-flow inconsistency and time-point inconsistency) to advance research in this field. Time-flow inconsistency is in line with the previous time inconsistency literature, while time-point inconsistency is rooted in the VC fund’s finite lifespan. Based on the assumption about the strategies guiding future behaviors, we consider four types of venture capitalists: time-consistent, time-point-inconsistent, naïve, and sophisticated venture capitalists, of which the latter three are time-inconsistent. We derive and compare the exit thresholds of these four types of venture capitalists. The main results include: (1) time-inconsistent preferences accelerate the exits of venture capitalists; (2) the closer the VC funds expiry dates are, the more likely time-inconsistent venture capitalists are to accelerate their exits; and (3) future selves caused by time-flow inconsistency weaken the effect of time-point inconsistency. Our study provides a behavioral explanation for the empirical fact of young VCs’ grandstanding.

The Study of Mean-Variance Risky Asset Management with State-Dependent Risk Aversion under Regime Switching Market

How do investors require a distribution of the wealth among multiple risky assets while facing the risk of the uncontrollable payment for random liabilities? To cope with this problem, firstly, this paper explores the approach of asset-liability management under the state-dependent risk aversion with only risky assets, which has been considered under a continuous-time Markov regime-switching setting. Next, based on this realistic modelling, an extended Hamilton-Jacob-Bellman (HJB) system has been necessarily established for solving the optimization problem of asset-liability management. It has been derived closed-form analytical expressions applied in the time-inconsistent investment with optimal control theory to see that happens to the optimal value of the function. Ultimately, numerical examples presented with comparisons of the analytical results under different market conditions are exposed to analyse numerically the developed mean variance asset liability management strategy. We find that our proposed model can explain the financial phenomena more effectively and accurately.

Time-Inconsistent Preferences and Strategic Self-Control in Digital Content Consumption

This study examines consumers’ time-inconsistent preferences in digital content consumption and their strategic self-control behaviors.

The Folk Theorem for Repeated Games with Time-Dependent Discounting

This paper defines a general framework to study infinitely repeated games with time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeated games, we introduce an asymptotic condition to characterize the fact that players become more and more patient; that is, the discount factors at all stages uniformly converge to one. Two types of folk theorems are proven without the public randomization assumption: the asymptotic one, that is, the equilibrium payoff set converges to the feasible and individual rational set as players become patient, and the uniform one, that is, any payoff in the feasible and individual rational set is sustained by a single strategy profile that is an approximate subgame perfect Nash equilibrium in all games with sufficiently patient discount factors. We use two methods for the study of asymptotic folk theorem: the self-generating approach and the constructive proof. We present the constructive proof in the perfect-monitoring case and show that it can be extended to time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a nonmonotonicity result.

A Resource Extraction Model with Technology Adoption under Time Inconsistent Preferences

A two-stage non-standard optimal control problem with time inconsistent preferences is studied. In an infinite horizon setting, a time consistent (sophisticated) decision maker chooses the time of switching between two consecutive regimes. The second regime corresponds to the implementation of a new technology, and a cost must be paid at the switching time. Although the problem is formulated for a general discount function, special attention is devoted to models with nonconstant discounting and heterogeneous discounting. The problem is solved by transforming it into a problem in a finite horizon and free terminal time. The corresponding dynamic programming equations are presented, and conditions for the derivation of the switching time by decision makers with different degrees of sophistication are studied. A resource extraction model with technology adoption is solved in detail. Effects of the adoption of different discount functions are illustrated numerically.

Consumption Threshold at Which Virtue Products Become Vice Products: The Case of Beer

Relative vices and virtues have traditionally been defined according to time-inconsistent preferences. Vice products exchange small immediate rewards (e.g., pleasure) for larger delayed costs (e.g., health), while virtue products exchange small immediate costs for larger delayed rewards. This definition can be criticized because there is evidence that small amounts of beer (or chocolate) convey a long-term health benefit, whereas large quantities impose a delayed cost. Thus, we assume that virtue products can become vice products when consumption is above a certain threshold. Survey data identifies alcoholic beer as a product that gives immediate rewards and does not impose a delayed cost. Our analysis reveals a consumption threshold that supports our assumptions.

Characterization of stochastic equilibrium controls by the Malliavin calculus

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.