Title: Time Consistent Mean-Variance Portfolio under Regime-Switching Cointegration

Abstract: Continuous-time cointegration models with constant parameters are shown to exhibit statistical arbitrage. However, the model parameters can change over time and the cointegration feature may even disappear due to regime shifts. This research investigates the optimal investment strategy under the Markov regime-switching cointegration models using a time-consistent mean-variance criterion. Explicit solution is derived for the optimal trading rule. We discuss the difficulty of computing the efficient frontier due to the Poisson random measure associated with the Markov regime-switching cointegration model. (This research is supported by the Research Grant Council of Hong Kong with GRF Project Number: 18200114.)

Title: Resolving Time Inconsistency via a Competition Scheme

Title: Dynamic Risk Measures and Nonlinear Expectations with Markov Chain Noise

Abstract: It is increasingly clear that a good understanding of risk and related dynamic models are required.. One aspect of this is the development of simple ways of numerically representing risk. Some of these ways are well known, for example, value at risk, expected shortfall, etc.. Unfortunately, these methods are static and fail to give consistent answers when considered at multiple time points. Progress has been made in developing dynamic risk measures, which give time consistent answers. Some of these ideas are related to the g-expectations considered by Peng and others. Central to the mathematical study of our consistent risk measures is the theory of Backward Stochastic Differential Equations (BSDEs). Most previous work in this area uses only noise from a Brownian motion. In our models the randomness is introduced through a martingale associated with a Markov chain. In particular we show that under certain conditions the solution to a BSDE is a time consistent risk measure.

Title: Time-Inconsistent Risk Preferences and the Term Structure of Dividend Strips

Abstract: I construct a general equilibrium model with time-inconsistent risk preferences to explain the downward-sloping term structure of dividend strips, an empirical pattern found by van Binsbergen et al. (2012). As risks draw temporally closer, investors will be increasingly driven by emotions, such as anxiety or excitement, which will distort their aversion to immediate risk, rendering it either higher or lower than their aversion to future risks. Dynamically, this leads to self-control problems. I explore its asset pricing implications and show that the term structures of dividend strips are downward-sloping when investors are less averse to immediate risk.

Title: Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers

Abstract: We consider a casino gambling model and study the strategies of a pre-committed gambler, who commits her future selves to the strategy she sets up today, and of a naive gambler, who fails to do so and thus keeps changing plans at every time. We identify conditions under which the pre-committed gambler, asymptotically, adopts a stop-loss strategy, exhibits the behavior of disposition effect, or does not exit. For a specific parameter setting when the utility function is piece-wise power and the probability weighting functions are concave power, we derive the optimal strategy of the pre-committed gambler in closed form whenever it exists. Finally, we study the actual behavior of the naive gambler and highlight its marked differences from that of the pre-committed gambler. This is a joint work with Sang Hu, Jan Obloj, and Xunyu Zhou.

Title: Self-Coordination in Time Inconsistent Stochastic Control: A Planner-Doer Game Framework

Abstract: Time inconsistency has been a thorny issue in many economic and financial decision making problems, especially when risk measures are involved in performance criteria. We develop in this research a two-tier planner–doer game framework with self-coordination. By aligning the global interest of the planner and the local interests of the doers by applying suitable penalty functions, a degree of internal harmony (measured quantitatively by the expected cost of self-coordination) can be achieved by the self-coordination policy. We establish an axiom system for modified preferences, under which the self-coordination policy can be obtained by solving a corresponding optimization problem. We then apply our game frame work successfully in dynamic mean-variance portfolio selection.

Title: A Mean-Field Competition

Abstract: We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. On the one hand, we propose a tractable Poissonian model in which we can characterize the optimal efforts for a given reward scheme. On the other hand, we study the principal agent problem of designing an optimal reward scheme. A surprising, explicit solution is found to minimize the time until a given fraction of the population has reached the goal. (Work-in-progress with Yuchong Zhang)

Title: The Monte Carlo-Based Stochastic Grid Bundling Method and Multi-period Mean-Variance Time-Consistent Portfolio Optimization

Abstract: In our research work we have developed an efficient Monte Carlo method for high-dimensional American options, called the Stochastic Grid Bundling Method (SGBM). We have developed this simulation-based approach further towards solving the constrained dynamic mean-variance portfolio management problem. We dealt with target-based as well as time-consistent problems with constraints. For these target-based and time-consistent dynamic optimization problems, we developed a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a forward fashion. It solves the unconstrained dynamic problem. Based on this fast yet sub-optimal strategy, we propose an approach to improve the solution, based on the backward recursive programming. In our numerical tests, highly satisfactory asset allocations can be achieved for the time-consistent dynamic portfolio management problem in case various constraints are cast on the control variables. We will explain our methodology and finding in the presentation.

Title: Time-Consistent Consumption and Investment

Abstract: We present some developments in consumption-investment problems with consistency issues. First, we review the mean-variance consumption-investment problems that have been studied in the recent literature. Second, we present some alternative quadratic objectives and present the corresponding optimal portfolios. Finally, we show how consistency issues show up also in utility optimization in case of non-linear aggregation of certainty equivalents of consumption.

Title: A Paradox in Time Consistency in Mean-Variance Problem?

Abstract: In this talk, we shall establish that, if investors with mean-variance preference adopt the time-consistent equilibrium solutions, an investor facing short-selling prohibition can acquire a greater objective value than his counterpart without the prohibition in a buoyant market. It can be shown that the pure strategy of solely investing on bond can sometimes simultaneously dominate the equilibrium strategy. With numerical experiments, the constrained investor can dominate the unconstrained one for more than 90% of the time horizon. The source of paradox is rooted from the nature of game-theoretic approach on time consistency, which purposely seeks for an equilibrium solution but not the ultimate maximizer. Our obtained results actually advocate that, to properly implement the concept of time consistency in various financial problems, all economic aspects should be critically taken into account at a time.

Title: Optimal Dividend Strategy for a General Diffusion Process with Time-Inconsistent Preferences and Penalty Cost for Ruin

Abstract: This paper considers the optimal dividend strategy for a company whose surplus follows a general diffusion process. The company's manager, who has time-inconsistent preferences, seeks the optimal dividend strategy and is subjected to a penalty cost when the company goes bankruptcy. We tackle the optimization problem by assuming that the manager is time-consistent, naive or sophisticated, and we obtain analytical solutions, respectively. Our results show that the sophisticated manager tends to pay out dividends earlier than the naive manager, who in turn tends to pay out dividends earlier than the time-consistent manager, and that managers with a higher level of time inconsistency tend to pay out dividends earlier; in contrasts, the penalty cost leads to delay in dividend payments. Finally, we provide several examples to illustrate our results. (Coauthors: Shumin Chen, Zhongfei Li)